Question

Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft

Answer 1

A = 52
`√(3)` ft² ≈ 90.1 ft²

Explanation:

the area (A) of a trapezoid is calculated as

A =
`(1)/(2)` h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4
`√(3)` , b₁ = 15 , b₂ = 11 , then

A =
`(1)/(2)` × 4
`√(3)` × (15 + 11)

= 2
`√(3)` × 26

= 52
`√(3)` ft²

≈ 90.1 ft² ( to the nearest tenth )

Answer 2

`52√(3) ft^(2)`

Explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x
`4√(3)`

`=44√(3) ft^(2)`

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

`0.5*4*4√(3) \\=8√(3) ft^(2)`

Area of Trapezoid = Area of Rectangle + Area of Triangle

`=44√(3) +8√(3) \\=52√(3) ft^(2)`