Question

These trapezoids are similar. Find the area of the larger trapezoid to the nearest whole number.

Answer 1

The area of larger trapezoid = 122 m²

Explanation:

It is given two similar trapezoids.

The length of small trapezoid =12 m

The length of larger trapezoid = 18 m

Area of small trapezoid = 54 m²

To find the area of larger trapezoid

We know that if two trapezoids are similar, then the ratio of its area is equal to square of its lengths.

Let L₁ be the length and A₁ be the area of small trapezoid and,

L₂ be the length and A₂ be the area of larger trapezoid.

L₁= 12 m, L₂ = 18 m A₁ = 54 m², A₂ = ?

A₁/A₂ = L₁²/L₂²

54/A₂ = 12²/18²

A₂ = 54 * 324/144

A₂ = 121.5 ≈ 122 ²

Answer 2

122 m²

Explanation:

We are given that the trapezoid are similar.

As we know, 'If the figures are similar, the ratio of their corresponding measurements are equal'.

Also, 'Area of trapezoids are quadratic relative to the lengths'.

So, we have,

Ratio of area of big and small trapezoid = Ratio of square of lengths of the trapezoid.

That is,

`(A_(B))/(A_(S))=((L_(B))^2)/((L_(S))^2)`

i.e.
`A_(B)=A_(S)* ((L_(B))^2)/((L_(S))^2)`

i.e.
`A_(B)=54* ((18)^2)/((12)^2)`

i.e.
`A_(B)=54* (324)/(144)`

i.e.
`A_(B)=54* 2.25`

i.e. Area of the big trapezoid = 121.5 m²

Hence, the area of the larger trapezoid to the nearest whole number is 122 m².