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MATHEMATICS FORMULA | KANUNI ZA HISABATI

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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. Squareformula1 Perimeter of Square.Perimeter = Side \times 4
2. Rectangleformula3 Perimeter of Rectangle.Perimeter = 2 \times (Length + Width)
3. Triangleformula23 Perimeter of Triangle.Perimeter = a + b + c

Perimeter = Total \; of \; lengths \; all\; three \;sides
4. Trapeziumformula24 Perimeter of Trapezium.Perimeter = a + b + c + d
5. Parallelogramformula25 Perimeter of Parallelogram.

Perimeter = a + b + c + d

6. Circleformula7 Circumference of Circle.

Circumf. = 2 \pi r \;\; OR \;\; Circumf. = \pi d

\pi = \frac{22}{7}, \;\; r = \frac{1}{2}diameter, \;\; d = diameter
7. Circleformula8 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 circleformula9 Circumference of quarter of circleCircumf. = \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 circleformula10 Circumference of three quarter of circleCircumf. = \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. Sectorformula11 Circumference of sectorMzingo = \frac{\pi r \theta}{180} + 2r\;\; OR \;\; Mzingo = \frac{\pi d \theta}{360} + d
NA. UMBO/MCHORO KANUNI
1. Squire | Mrabaformula1 AREA | Eneo la MrabaEneo = Upande \times Upande
2. DIAGONAL | Mraba wenye ulalo formula2 AREA OF DIAGONAL | Eneo la Mraba iwapo umepewa ulaloEneo =( \frac{1}{2} \times ZO \times WY) \times 2
3. RECTANGLE | Mstatiliformula3 ARES OF A RECTANGLE ” Eneo la Mstatili.Eneo = Urefu \times Upana
4. TRIANGLE | Pembetatuformula4 AREA OF A TRINGLE | Eneo la Pembetatu.Eneo = \frac{1}{2} bh

b = kitako \; \; h = kimo
5. SHADE TRIANGLE | Pembetatu yenye kivuliformula5 AREA OF A SHADE TRIANGLE | Eneo lililotiwa kivuliEneo \; 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)formula6 AREA OF A TRAPEZZA | Eneo la trapeza (tenge)Eneo = \frac{1}{2}(a + b)h
7. PARALLEL | Msambambaformula21 AREA OF PARALLEREneo la msambamba.Eneo = bh
8. CIRCLE | Duaraformula7 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 duaraformula8 AREA OF HALF CIRCLE | Eneo la nusu duaraEneo = \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 duaraformula9 AREA OF  QUATER CIRCLEEneo la robo duaraEneo = \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

formula10

 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 | Sektaformula11 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 kivulieneo3 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 mstatiliformula20 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.formula17 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 mmojaformula19 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 zoteformula18 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 pembetatuformula13 AREA | Eneo la mche pembetatuEneo = [E \Delta (ABE) \times 2 ]+ [E(ABCF) \times 2] + [E(AEDF) \times 2] + [E(EBCDE)\times 2]
5. SQUIRE | Mche mrabaformula22 AREA OF SQUIRE | Eneo la mche mraba.Eneo = (Up. \times Up. \times 6)

CIRCLES | MIZUNGUUKO

NA. SHAPE/UMBO/MCHORO  PRINCIPLES | KANUNI
1. SQUIRE | Mrabaformula1 Mzingo wa Mraba.Mzingo = Upande \times 4
2. RECTANGLE | Mstatiliformula3 Mzingo wa Mstatili.Mzingo = 2 \times (Urefu + Upana)
3. TRIANGLE | Pembetatuformula23 TRIANGLE | Mzingo wa Pembetatu.Mzingo = a + b + c

Mzingo = Jumla \; ya \; urefu \; wa \; pande \; zote \; tatu
4. TRAPEZZA | Trapezaformula24 TRAPEZZA | Mzingo wa Trapeza.Mzingo = a + b + c + d
5. PARALLEL | Msambambaformula25 PARALLEL | Mzingo wa MsambambaMzingo = a + b + c + d
6. CIRCLE | Duaraformula7 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 Duaraformula8 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 duaraformula9 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 duaraformula10 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 | Sektaformula11 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 Mrabaformula22 SQUIRE | Ujazo la Mche Mraba.

Ujazo = Up. \times Up. \times Up.
2. RECTANGLE | Mche Mstatiliformula20  RECTANGLE | Ujazo wa Mche Mstatili.

Ujazo = Ur. \times Up. \times h.
3. CIRCLE | Mche Duaraformula18 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 | Piaformula14 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 Mstatiliformula15 PYRAMID | Ujazo Piramidi yenye kitako cha MstatiliUjazo = \frac{1}{3} \times (Urefu \times Upana \times Kimo)
6. SQUIRE BASE PYRAMID | Piramidi yenye kitako cha Mrabaformula26 SQUIRE BASE PYRAMID | Ujazo Piramidi yenye kitako cha Mraba.Ujazo = \frac{1}{3} \times (Upana \times Upana \times Kimo)
7. GLOBE | Tufe

formula16

 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 | Mwendoformula27 SPEED | MwendoUmbali = 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 Pythagorasformula23 PYTHAGORAS THEOREAM | Kanuni za Pythagorasc^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.formula28

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.formula29

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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