Question

A and b are two similar 2D shapes. The area of shape awhich is 12cm is 200cm squared. Calculate the area of shape b which is 15cm

Answer 1

Answer: Area of shape which is 15 cm is 312.5 square cm.

Step-by-step explanation:

Since we have given that

Area of shape of 12 cm = 200 sq. cm

We need to find the area of shape of 15 cm.

As we know the "Area similarity theorem" which states that ratio of areas of two similar shapes is equal to the square of ratio of corresponding sides.

So, it becomes,

$\dfrac{12^2}{15^2}=\dfrac{200}{x}\\\\\dfrac{144}{225}=\dfrac{200}{x}\\\\144x=200\times 225\\\\144x=45000\\\\x=\dfrac{45000}{144}\\\\x=312.5\ cm^2$

So, Area of shape which is 15 cm is 312.5 square cm.

Answer 2

Answer:

The area of b = 312.50 cm^2.

Step-by-step explanation:

The areas are in the ratio (a / b) = 12^2  / 15^2 = 144/225, so we have the equation

200/b  = 144/225 where b is the area of shape b.

b =  200 * 225 / 144

b = 312.50.