Question

Pentagons T and U are similar. The area of T is 17 cm². Calculate the area of U. 4 cm T 3 cm U 12 cm 20 cm Not drawn accurately​

Answer 1

The area of pentagon U in the image given below is calculated as: 272 cm².

What is the area of similar pentagons?

The area of similar figures (including pentagons) is proportional to the square of their corresponding linear dimensions (such as side lengths). If the ratio of corresponding sides of two similar pentagons is k, then the ratio of their areas is
`k^2`.

17 cm² is the area of pentagon T and let x be the area of pentagon U, and 3 and 12 are the lengths of their corresponding sides, then:

`(17)/(x) = \left((3)/(12)\right)^2`

Solve for x:

17/x = 9/144

9x = 17 * 144

9x = 2,448

x = 2,448/9

x = 272

Area of pentagon U = 272 cm².