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 = [tex]\frac{1}{2} \times \text{sum of the parallel side}\times \text{height}[/tex]
[tex]$=\frac{1}{2}\times (10 + 12 ) \times h[/tex]
[tex]$=\frac{1}{2}\times 22 \times h[/tex]
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
