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# 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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