MATHEMATICS FORMULA | KANUNI ZA HISABATI

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MATHEMATICS FORMULA | KANUNI ZA HISABATI

Here you can get formula and solutions to different problems for mathematics

FORMULA FOR CALCULATING AREAS OF PLANE SHAPES | KANUNI ZA KUTAFUTA MAENEO YA MAUMBO

S/N.	SHAPE/FIGURE	FORMULA
1.	Square	Perimeter of Square. $Perimeter = Side \Times 4$
2.	Rectangle	Perimeter of Rectangle. $Perimeter = 2 \Times (Length + Width)$
3.	Triangle	Perimeter of Triangle. $Perimeter = A + B + C$ $Perimeter = Total \; Of \; Lengths \; All\; Three \;Sides$
4.	Trapezium	Perimeter of Trapezium. $Perimeter = A + B + C + D$
5.	Parallelogram	Perimeter of Parallelogram. $Perimeter = A + B + C + D$
6.	Circle	Circumference of Circle. $Circumf. = 2 \Pi R \;\; Or \;\; Circumf. = \Pi D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Diameter, \;\; D = Diameter$
7.	Circle	Circumference of semi circle. $Circumf. = \Pi R + 2R\;\; Or \;\; Circumf. = \Frac{1}{2} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Diameter, \;\; D = Diameter$
8.	Quarter of circle	Circumference of quarter of circle $Circumf. = \Frac{1}{2} \Pi R + 2R\;\; Or \;\; Circumf. = \Frac{1}{4} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Diameter, \;\; D = Diameter$
9.	Three quarter of circle	Circumference of three quarter of circle $Circumf. = \Frac{3}{2} \Pi R + 2R\;\; Or \;\; Circumf. = \Frac{3}{4} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Diameter, \;\; D = Diameter$
10.	Sector	Circumference of sector $Mzingo = \Frac{\Pi R \Theta}{180} + 2R\;\; Or \;\; Mzingo = \Frac{\Pi D \Theta}{360} + D$

NA.	UMBO/MCHORO	KANUNI
1.	Squire \| Mraba	AREA \| Eneo la Mraba $Eneo = Upande \Times Upande$
2.	DIAGONAL \| Mraba wenye ulalo	AREA OF DIAGONAL \| Eneo la Mraba iwapo umepewa ulalo $Eneo =( \Frac{1}{2} \Times Zo \Times Wy) \Times 2$
3.	RECTANGLE \| Mstatili	ARES OF A RECTANGLE ” Eneo la Mstatili. $Eneo = Urefu \Times Upana$
4.	TRIANGLE \| Pembetatu	AREA OF A TRINGLE \| Eneo la Pembetatu. $Eneo = \Frac{1}{2} Bh$ $B = Kitako \; \; H = Kimo$
5.	SHADE TRIANGLE \| Pembetatu yenye kivuli	AREA OF A SHADE TRIANGLE \| Eneo lililotiwa kivuli $Eneo \; Lililotiwa \; Kivuli= Eneo \; La \; \Delta (Wxz) \; Kutoa \; Eneo \; La \; \Delta (Wyz)$ $Eneo \; Lililotiwa \; Kivuli= \Frac{1}{2}(A + B)H - \Frac{1}{2} Ah$ Au $Eneo \; Lililotiwa \; Kivuli= \Frac{1}{2} Bh$
6.	TRAPEZZA \| Trapeza (tenge)	AREA OF A TRAPEZZA \| Eneo la trapeza (tenge) $Eneo = \Frac{1}{2}(A + B)H$
7.	PARALLEL \| Msambamba	AREA OF PARALLEREneo la msambamba. $Eneo = Bh$
8.	CIRCLE \| Duara	AREA OF A CIRCLE \| Eneo la duara. $Eneo = \Pi R^2 \; \; Au \; \; Eneo = \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
9.	HALF ACIRCLE \| Nusu duara	AREA OF HALF CIRCLE \| Eneo la nusu duara $Eneo = \Frac{1}{2} \Pi R^2 \; \; Au \; \; Eneo = \Frac{1}{2} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
10.	QUATER CIRCLE \| Robo duara	AREA OF QUATER CIRCLEEneo la robo duara $Eneo = \Frac{1}{4} \Pi R^2 \; \; Au \; \; Eneo = \Frac{1}{4} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
11.	THREE-QUARTER CIRCLE \| Robo tatu duara	AREA OF THREE-QUARTER CIRCLE \| Eneo la robo tatu duara. $Eneo = \Frac{3}{4} \Pi R^2 \; \; Au \; \; Eneo = \Frac{3}{4} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
12.	SECTOR \| Sekta	AREA OF A SECTOR \| Eneo la secta. $Eneo = \Frac{\Theta}{360} \Pi R^2 \; \; Au \; \; Eneo = \Frac{\Theta}{360} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
13.	SHADED AREA \| Eneo lililotiwa kivuli	SHADED AREA \| Eneo la secta. $Eneo = \Pi R^2 - \Pi R^2\;\;Au\;\;Eneo = \Frac{\Pi D^2}{4} - \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}\;\;Kipenyo, \; \; D = Kipenyo.$

HOW TO FIND AREAS OF DIFFERENT SHAPES | KANUNI ZA KUTAFUTA MAENEO YA NYUSO ZA MAUMBO YA UKUMBI

NA.	SHAPE/UMBO/MCHORO	PRINCIPLES \| KANUNI
1.	RECTANGLE \| Mche mstatili	AREA OF A RECTANGLE \| Eneo la mche mstatili. $Eneo = (Ur. \Times Up. \Times 2) + (Ur. \Times H \Times 2) + (Up. \Times H \Times 2)$ $Ur. = Urefu, \;\; Up. = Upana, \;\; H = Kimo$
2.	CIRCLE \| Mche duara ulio wazi pande zote.	AREA \| Eneo la mche duara ulio wazi pande zote. $Eneo = 2 \Pi Rh \;\; Au \;\; Eneo = \Pi Dh$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
3.	CLOSED SIDE CIRCLE \| Mche duara uliozibwa upande mmoja	AREA OF CLOSED SIDE CIRCLE \| Eneo la mche duara uliozibwa upande mmoja. $Eneo = 2 \Pi Rh + \Pi R^2 \;\; Au \;\; Eneo = \Pi Dh + \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
4.	CIRCLE CLOSED ALL SIDES \| Mche duara uliozibwa pande zote	AREA OF CIRCLE CLOSED ALL SIDES \| Eneo la mche duara uliozibwa pande zote. $Eneo = 2 \Pi Rh + 2 \Pi R^2 \;\; Au \;\; Eneo = \Pi Dh + 2 \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
5.	TRIANGLE \| Mche pembetatu	AREA \| Eneo la mche pembetatu $Eneo = [E \Delta (Abe) \Times 2 ]+ [E(Abcf) \Times 2] + [E(Aedf) \Times 2] + [E(Ebcde)\Times 2]$
5.	SQUIRE \| Mche mraba	AREA OF SQUIRE \| Eneo la mche mraba. $Eneo = (Up. \Times Up. \Times 6)$

CIRCLES | MIZUNGUUKO

NA.	SHAPE/UMBO/MCHORO	PRINCIPLES \| KANUNI
1.	SQUIRE \| Mraba	Mzingo wa Mraba. $Mzingo = Upande \Times 4$
2.	RECTANGLE \| Mstatili	Mzingo wa Mstatili. $Mzingo = 2 \Times (Urefu + Upana)$
3.	TRIANGLE \| Pembetatu	TRIANGLE \| Mzingo wa Pembetatu. $Mzingo = A + B + C$ $Mzingo = Jumla \; Ya \; Urefu \; Wa \; Pande \; Zote \; Tatu$
4.	TRAPEZZA \| Trapeza	TRAPEZZA \| Mzingo wa Trapeza. $Mzingo = A + B + C + D$
5.	PARALLEL \| Msambamba	PARALLEL \| Mzingo wa Msambamba $Mzingo = A + B + C + D$
6.	CIRCLE \| Duara	Mzingo wa Duara. $Mzingo = 2 \Pi R \;\; Au \;\; Mzingo = \Pi D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
7.	HALF CIRCLE \|NUSU Duara	HALF CIRCLE \| Mzingo wa nusu duara. $Mzingo = \Pi R + 2R\;\; Au \;\; Mzingo = \Frac{1}{2} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
8.	QUATER CIRLCE \| Robo duara	QUATER CIRLCE \| Mzingo wa robo duara. $Mzingo = \Frac{1}{2} \Pi R + 2R\;\; Au \;\; Mzingo = \Frac{1}{4} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
9.	THREE QUATER \| Robo tatu duara	THREE QUATER \| Mzingo wa robo tatu duara. $Mzingo = \Frac{3}{2} \Pi R + 2R\;\; Au \;\; Mzingo = \Frac{3}{4} \Pi D + D$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
10.	SECTOR \| Sekta	Mzingo wa robo sekta. $Mzingo = \Frac{\Pi R \Theta}{180} + 2R\;\; Au \;\; Mzingo = \Frac{\Pi D \Theta}{360} + D$

CUBIC | UJAZO / UKUBWA

NA.	SHAPE/UMBO/MCHORO	PRINCIPLES \| KANUNI
1.	SQUIRE \| Mche Mraba	SQUIRE \| Ujazo la Mche Mraba. $Ujazo = Up. \Times Up. \Times Up.$
2.	RECTANGLE \| Mche Mstatili	RECTANGLE \| Ujazo wa Mche Mstatili. $Ujazo = Ur. \Times Up. \Times H.$
3.	CIRCLE \| Mche Duara	CIRCLE \| Ujazo wa Mche Duara. $Ujazo = \Pi R^2 H \;\; Au \;\; Ujazo = \Frac{\Pi D^2 H}{4}$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
4.	PI \| Pia	Ujazo Pia. $Ujazo = \Frac{1}{3} \Pi R^2 H \;\; Au \;\; Ujazo =\Frac{1}{3} \Frac{\Pi D^2 H}{4}$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
5.	PYRAMID \| Piramidi yenye kitako cha Mstatili	PYRAMID \| Ujazo Piramidi yenye kitako cha Mstatili $Ujazo = \Frac{1}{3} \Times (Urefu \Times Upana \Times Kimo)$
6.	SQUIRE BASE PYRAMID \| Piramidi yenye kitako cha Mraba	SQUIRE BASE PYRAMID \| Ujazo Piramidi yenye kitako cha Mraba. $Ujazo = \Frac{1}{3} \Times (Upana \Times Upana \Times Kimo)$
7.	GLOBE \| Tufe	GLOBE \| Ujazo wa Tufe. $Ujazo = \Frac{4 \Pi R^3}{3} \;\; Au \;\; Ujazo = \Frac{\Pi D^3}{6}$

OTHER MATHEMATICS PRINCIPLES | KANUNI NYINGINEZO

NA.	SHAPE/UMBO/MCHORO	PRINCIPLE \| KANUNI
1.	SPEED \| Mwendo	SPEED \| Mwendo $Umbali = Mwendokasi \Times Muda$ $Mwendokasi = \Frac{Umbali}{Muda}$ $Muda = \Frac{Umbali}{Mwendokasi}$
2.	INTERST \| Riba katika benki	INTERST \| Riba katika benki. $I = \Frac{Prt}{100}$ $P = \Frac{100I}{Rt}$ $R = \Frac{100I}{Pt}$ $T = \Frac{100I}{Pr}$ $P = Kianzio, \; R = Kiasi, \; T = Muda, \; I = Faida$
3.	PYTHAGORAS THEOREAM \| Kanuni za Pythagoras	PYTHAGORAS THEOREAM \| Kanuni za Pythagoras $C^2 = A^2 + B^2$ $A = \Sqrt{C^2 - B^2}$ $B = \Sqrt{C^2 - A^2}$ $C = \Sqrt{A^2 + B^2}$
4.	Umbo lenye pande ‘n’ zenye urefu sawa. Katika umbo hili “n=6”	Jumla ya pembe za ndani za umbo lenye pande ‘n’ zenye urefu sawa. $Jumla \; Ya \; Pembe = (N-2)\Times 180^0$ $N = Idadi \; Ya \; Pande \; Za \; Umbo$
5.	Thamani ya pembe ya nje ya umbo lenye pande ‘n’ zenye urefu sawa. Katika umbo hili “n=6”	Thamani ya pembe ya nje ya umbo lenye pande ‘n’ zenye urefu sawa. $Thamani\;Ya\;Pembe (X) = \Frac {360^0}{N}$ $N = Idadi \; Ya \; Pande \; Za \; Umbo$

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NA.	UMBO/MCHORO	KANUNI
1.	Squire \| Mraba	AREA \| Eneo la Mraba $Eneo = Upande \Times Upande$
2.	DIAGONAL \| Mraba wenye ulalo	AREA OF DIAGONAL \| Eneo la Mraba iwapo umepewa ulalo $Eneo =( \Frac{1}{2} \Times Zo \Times Wy) \Times 2$
3.	RECTANGLE \| Mstatili	ARES OF A RECTANGLE ” Eneo la Mstatili. $Eneo = Urefu \Times Upana$
4.	TRIANGLE \| Pembetatu	AREA OF A TRINGLE \| Eneo la Pembetatu. $Eneo = \Frac{1}{2} Bh$ $B = Kitako \; \; H = Kimo$
5.	SHADE TRIANGLE \| Pembetatu yenye kivuli	AREA OF A SHADE TRIANGLE \| Eneo lililotiwa kivuli $Eneo \; Lililotiwa \; Kivuli= Eneo \; La \; \Delta (Wxz) \; Kutoa \; Eneo \; La \; \Delta (Wyz)$ $Eneo \; Lililotiwa \; Kivuli= \Frac{1}{2}(A + B)H - \Frac{1}{2} Ah$ Au $Eneo \; Lililotiwa \; Kivuli= \Frac{1}{2} Bh$
6.	TRAPEZZA \| Trapeza (tenge)	AREA OF A TRAPEZZA \| Eneo la trapeza (tenge) $Eneo = \Frac{1}{2}(A + B)H$
7.	PARALLEL \| Msambamba	AREA OF PARALLEREneo la msambamba. $Eneo = Bh$
8.	CIRCLE \| Duara	AREA OF A CIRCLE \| Eneo la duara. $Eneo = \Pi R^2 \; \; Au \; \; Eneo = \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
9.	HALF ACIRCLE \| Nusu duara	AREA OF HALF CIRCLE \| Eneo la nusu duara $Eneo = \Frac{1}{2} \Pi R^2 \; \; Au \; \; Eneo = \Frac{1}{2} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
10.	QUATER CIRCLE \| Robo duara	AREA OF QUATER CIRCLEEneo la robo duara $Eneo = \Frac{1}{4} \Pi R^2 \; \; Au \; \; Eneo = \Frac{1}{4} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
11.	THREE-QUARTER CIRCLE \| Robo tatu duara	AREA OF THREE-QUARTER CIRCLE \| Eneo la robo tatu duara. $Eneo = \Frac{3}{4} \Pi R^2 \; \; Au \; \; Eneo = \Frac{3}{4} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
12.	SECTOR \| Sekta	AREA OF A SECTOR \| Eneo la secta. $Eneo = \Frac{\Theta}{360} \Pi R^2 \; \; Au \; \; Eneo = \Frac{\Theta}{360} \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
13.	SHADED AREA \| Eneo lililotiwa kivuli	SHADED AREA \| Eneo la secta. $Eneo = \Pi R^2 - \Pi R^2\;\;Au\;\;Eneo = \Frac{\Pi D^2}{4} - \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}\;\;Kipenyo, \; \; D = Kipenyo.$

NA.	SHAPE/UMBO/MCHORO	PRINCIPLES \| KANUNI
1.	RECTANGLE \| Mche mstatili	AREA OF A RECTANGLE \| Eneo la mche mstatili. $Eneo = (Ur. \Times Up. \Times 2) + (Ur. \Times H \Times 2) + (Up. \Times H \Times 2)$ $Ur. = Urefu, \;\; Up. = Upana, \;\; H = Kimo$
2.	CIRCLE \| Mche duara ulio wazi pande zote.	AREA \| Eneo la mche duara ulio wazi pande zote. $Eneo = 2 \Pi Rh \;\; Au \;\; Eneo = \Pi Dh$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
3.	CLOSED SIDE CIRCLE \| Mche duara uliozibwa upande mmoja	AREA OF CLOSED SIDE CIRCLE \| Eneo la mche duara uliozibwa upande mmoja. $Eneo = 2 \Pi Rh + \Pi R^2 \;\; Au \;\; Eneo = \Pi Dh + \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
4.	CIRCLE CLOSED ALL SIDES \| Mche duara uliozibwa pande zote	AREA OF CIRCLE CLOSED ALL SIDES \| Eneo la mche duara uliozibwa pande zote. $Eneo = 2 \Pi Rh + 2 \Pi R^2 \;\; Au \;\; Eneo = \Pi Dh + 2 \Frac{\Pi D^2}{4}$ $\Pi = \Frac{22}{7}, \; \; R = \Frac{1}{2}Kipenyo, \; \; D = Kipenyo.$
5.	TRIANGLE \| Mche pembetatu	AREA \| Eneo la mche pembetatu $Eneo = [E \Delta (Abe) \Times 2 ]+ [E(Abcf) \Times 2] + [E(Aedf) \Times 2] + [E(Ebcde)\Times 2]$
5.	SQUIRE \| Mche mraba	AREA OF SQUIRE \| Eneo la mche mraba. $Eneo = (Up. \Times Up. \Times 6)$

NA.	SHAPE/UMBO/MCHORO	PRINCIPLES \| KANUNI
1.	SQUIRE \| Mche Mraba	SQUIRE \| Ujazo la Mche Mraba. $Ujazo = Up. \Times Up. \Times Up.$
2.	RECTANGLE \| Mche Mstatili	RECTANGLE \| Ujazo wa Mche Mstatili. $Ujazo = Ur. \Times Up. \Times H.$
3.	CIRCLE \| Mche Duara	CIRCLE \| Ujazo wa Mche Duara. $Ujazo = \Pi R^2 H \;\; Au \;\; Ujazo = \Frac{\Pi D^2 H}{4}$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
4.	PI \| Pia	Ujazo Pia. $Ujazo = \Frac{1}{3} \Pi R^2 H \;\; Au \;\; Ujazo =\Frac{1}{3} \Frac{\Pi D^2 H}{4}$ $\Pi = \Frac{22}{7}, \;\; R = \Frac{1}{2}Kipenyo, \;\; D = Kipenyo$
5.	PYRAMID \| Piramidi yenye kitako cha Mstatili	PYRAMID \| Ujazo Piramidi yenye kitako cha Mstatili $Ujazo = \Frac{1}{3} \Times (Urefu \Times Upana \Times Kimo)$
6.	SQUIRE BASE PYRAMID \| Piramidi yenye kitako cha Mraba	SQUIRE BASE PYRAMID \| Ujazo Piramidi yenye kitako cha Mraba. $Ujazo = \Frac{1}{3} \Times (Upana \Times Upana \Times Kimo)$
7.	GLOBE \| Tufe	GLOBE \| Ujazo wa Tufe. $Ujazo = \Frac{4 \Pi R^3}{3} \;\; Au \;\; Ujazo = \Frac{\Pi D^3}{6}$

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