Question

What is the area of triangle DEF

Answer 1

76.5 cm²

Explanation:

Given the triangles are similar , then

ratio of sides = a : b , so

ratio of areas = a² : b²

Here ratio of sides = 9 : 13.5 = 2 : 3

ratio of areas = 2² : 3² = 4 : 9

let x be the area of Δ DEF and using proportion

`(4)/(34)` =
`(9)/(x)` ( cross- multiply )

4x = 306 ( divide both sides by 4 )

x = 76.5

The area of Δ DEF = 76.5 cm²