Trapezoid Height Calculation: Find h When Area = 30cm² (4cm & 8cm Parallel Sides)

Question

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

00:00 Find the height of the trapezoid

00:03 We'll use the formula for calculating the area of a trapezoid

00:06 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2

00:13 We'll substitute appropriate values and solve for the height

00:32 And this is the solution to the question

We use the formula to calculate the area: (base+base) times the height divided by 2

We replace the existing data:

$S=\frac{(AB+CD)\times h}{2}$

$30=\frac{(4+8)\times h}{2}$

We multiply the equation by 2:

$60=(4+8)h$

$60=12h$

We divide the two sections by 12:

$\frac{60}{12}=h$

$5=h$