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

The area of shape B which is of 15 $\text{cm}$, is 312.5 $\text{cm}^2$.

Given information:

The two shapes A and B are given

The dimensions of shape A is 12 $\text{cm}$

The area of the shape A is 200 $\text{cm}^2$

Now, we need to calculate the area of the shape of 15 $\text{cm}$

As we know that area will be square of the given values in the question.

So, according to the question:

$\frac{A^2}{B^2} =\frac{200}{x}$

$\frac{12^2}{15^2} =\frac{200}{x}\\\\\frac{144}{225}=\frac{200}{x} \\\\x=(200\times 225)/144\\\\x=312.5 \text{cm}^2$

Hence, the area of shape B which is of 15 cm, is 312.5 $\text{cm}^2$.

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