How to Do Math Area Formulas

For each math area formulas I have given a working example with answers, and as always some questions to try.

Math Area Formulas:










Square



Area = Length × Length

or using shorthand (because sometimes Mathematicians are just lazy)

A=L×L






Example 1: Find the area of a square, when the length is 4cm


Area = Length × Length or A=L×L

Area = 4 × 4

= 16cm2



Questions to try:


A) Find the area of these squares with the following lengths,


1. 6m (give your answer in cm)

2. 9cm

3. 2.5m (give your answer in cm)



(Answers are at the bottom as usual)










Rectangle



Area = Height × Base

or

A=H×B


Sometimes, you may see the math area formulas written as Length × Width. It all depends what you want to call the sides of your shape.

It does not matter what you call them. What matters is that you understand you are multiplying one side of the rectangle by the other side.






Example 2: Find the area of a rectangle, when the height is 3cm and base is 7cm.


Area = Height × Base or using shorthand letters A=H×B

Area = 3 × 7

= 21cm2



Questions to try:


B) Find the area of these rectangles when,

1. H=4m, B=6m

2. H=2km, B=8km

3. H=5cm, B=10cm



(Answers are at the bottom)






Triangle



Area=12×Base×Height

or

1⁄2×B×H





Example 3: Find the area of a triangle, when the height is 5cm and base is 7cm.

Area = 12×Base×Height or using shorthand letters only A= 12×B×H

Area = 12×7× 5

= 17.5cm2



C) Find the area of these triangles when,

1. H=6mm, B=3mm

2. H=4km, B=5km

3. H=100cm, B=3cm



(Answers are at the bottom)










Circle





Area=Π×radius×radius

or writing it shorthand is

A=Π×r2






Example 4: Find the area of a circle when the radius is 4cm.

Area=Π×radius×radius or using letters only A=Π×r2

A=Π×42=3.14×4×4=50.24cm2



Questions to try:

D) Find the math area formulas of these circles when the radius is,

1. r=7m

2. r=25cm

3. r=3.2mm



(Answers are at the bottom)










Example 5: Find the area of a circle when the diameter is 10cm.

The radius is half of the diameter. Therefore, if the diameter is 10cm the radius is 5cm

A=Ππ×r2

A=Π×52=3.14×5×5=78.5cm2



Questions to try:

E) Find the area of these circles when the diameter is,

1. d=8m

2. d=25cm

3. d=16mm



(Answers are at the bottom)




Trapezium





Area=[(Length of a + Length of b)×Height]/2

or

A=[(a+b)×H]/2

First add the lengths of a and b. Then multiply it with the height. Finally divide it by 2.






Example 6: Find the area of a trapezium when the length of a is 2cm, the length of b is 10cm and the height is 4cm

a=2, b=10, h=4

A=[(a+b)×H]/2

A=[(2+10)×4]/2

=48/2

=24cm2



Questions to try:

F) Find the area of the trapezium (in cm) when,

1. a=4, b=8, h=3

2. a=5, b=10, h=4

3. a=3, b=20, h=5




Parallelogram

Area=Base×Height

or

A=B×H






Example 7: Find the area of a parallelogram when the base is 6cm and the height is 5cm.

A=B×H

A=6×5=30cm2



Questions to try:

G) Find the math area formulas of the paralellogram (in cm) when,

1. B=10, H=6

2. B=8, H=9

3. B=20, H=7



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Answers



A)

1. L=6m, 6×6=36m2 which is 360cm2

2. L=9cm, 9×9=81cm2

3. L=2.5m, 2.5×2.5=6.25m2 which is 625cm2

B)

1. H=4m, L=6m, 4×6=24m2

2. H=2km, L=8km, 2×8=16km2

3. H=5cm, L=10cm, 5×10=50cm2

C)

1. H=6mm, B=3mm, 6×3=18/2= 9mm2

2. H=4km, B=5km, 4×5=20/2= 10km2

3. H=100cm, B=3cm, 100×3=300/2=150cm2









D)

1. r=7m, A=Π×72=3.14×7×7=153.9m2

2. r=25cm, A=Π×252=3.14×25×25=1963.4cm2

3. r=3.2mm, A=Π×3.22=3.14×3.2×3.2=32.16cm2

E)

1. d=8m, A=Π×42=3.14×4×4=50.26m2

2. d=25cm, A=Π×12.52=3.14×12.5×12.5=490.87cm2

3. d=16mm, A=Π×82=3.14×8×8=201.06mm2



F)

1. a=4, b=8, h=3, A=[(4+8)×3]/2=18cm2

2. a=5, b=10, h=4, A=[(5+10)×4]/2=35cm2

3. a=3, b=20, h=5, A=[(3+20)×5]/2=57.5cm2



G)

1. B=10, H=6, A=10×6=60cm2

2. B=8, H=9, A=8×9=72cm2

3. B=20, H=7, A=20×7=140cm2





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