Question

The polygons are similar. The area of one polygon is given. Find the area of the other polygon.

Answer 1

The area of the other polygon is $30 cm^2$

explanation

If two triangles are similar , then the ratio of their corresponding sides will be equal to the ratio of their areas. Here the given triangles are similar which means the ratio of their areas will be equal to the ratio of their corresponding sides.

The side length of the first triangle=4cm

Side length of the second triangle=12 cm

Area of the first triangle=$10cm^2$

Let the area of the second triangle be A/

$4/12=10/A\\A=(10*12)/4=120/4=30$

The area of the second triangle =$30cm^2$

Answer 2

The area of the other polygon is $\rm 30 cm^2$ and it can be determined by using a trigonometric ratio.

Given that,

The area of the first polygon is 10 square centimeters,

And the length of one side is 4 cm.

The side length of the second polygon is 12cm.

We have to determine

The area of the other polygon.

According to the question,

To determine the area of the second polygon following all the steps given below.

If the first polygon is similar to the other polygon then the ratio between the area of the first polygon and the side length is equal to the area of the other polygon and side length.

Then,

$\rm \dfrac{A_1}{S_1} = \dfrac{A_2}{S_2}$

Where $\rm A_1$ is the area of the first polygon and $\rm S_1$ is the side length of the first polygon.

And $\rm A_2$ is the area of the second polygon and $\rm S_2$ is the side length of the second polygon.

Substitute all the values in the equation.

$\rm \dfrac{A_1}{S_1} = \dfrac{A_2}{S_2}\\\\\rm \dfrac{10}{4} = \dfrac{A_2}{12}\\\\A_2 = \dfrac{10 \times 12}{4}\\\\A_2 = 10 \times 3\\\\A_2 = 30 \ cm^2$

Hence, The required area of the second polygon is $\rm 30 cm^2$.

To know more about Polygon refer to the link given below.

https://brainly.com/question/15442893