How do you find the area of a 2d shape

Asked by admin @ 29/10/2021 in Mathematics viewed by 297 People

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

Answered by admin @ 29/10/2021

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.

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