Question

Composite shape has an area of 162 cm squared. what is the height of the trapezoid

Answer 1

Answer: 6 cm

Explanation:

Answer 2

The height of the trapezoid = 6 cm

Solution:

The composite figure is splitted into two shapes.

One is rectangle and the other is trapezoid.

Area of the rectangle = length × width

= 12 cm × 8 cm

Area of the rectangle = 96 cm²

Area of the trapezoid =
`(1)/(2) * \text{sum of the parallel side}* \text{height}`

`$=(1)/(2)* (10 + 12 ) * h`

`$=(1)/(2)* 22 * h`

Area of the trapezoid = 11 h cm²

Area of the composite shape = 162 cm²

⇒ 96 + 11 h = 162

Subtract 96 on both sides of the equation.

⇒ 11 h = 162 – 96

⇒ 11 h = 66

Divide by 11 on both sides of the equation.

⇒ h = 6 cm

The height of the trapezoid = 6 cm