Trapezoid Base Calculation: Finding Bases Given Area 30 cm² and Height 5cm

Question

Given the trapezoid ABCD whose area is equal to 30 cm².

Side AB is equal to half of side DC

The height of the trapezoid is equal to 5cm

How much are the trapeze bases worth?

00:00 Find the bases of trapezoid AB and DC

00:04 Use the formula for calculating trapezoid area

00:08 (Sum of bases(AB+DC) times height(H)) divided by 2

00:12 Substitute appropriate values and solve for DC

00:17 We substituted AB with its size relative to DC according to the given data

00:20 Multiply by 2 to eliminate the fraction

00:25 Isolate DC

00:36 Multiply by the reciprocal to get DC

00:42 This is the size of DC

00:45 Now substitute this size in the sides ratio to find AB

00:52 And this is the solution to the question

To solve for the bases of the trapezoid, follow these steps:

Let the length of $AB$ be $x$ cm, and since $AB$ is half of $DC$ , let $DC$ be $2x$ cm.
Using the formula for the area of a trapezoid:

\text{Area} = \frac{1}{2} \times (AB + DC) \times \text{height}

\frac{1}{2} \times (x + 2x) \times 5 = 30

x

\frac{1}{2} \times 3x \times 5 = 30

7.5x = 30

x = \frac{30}{7.5} = 4

AB = x = 4 \, \text{cm}

DC = 2x = 8 \, \text{cm}

Therefore, the lengths of the trapezoid's bases are $AB = 4 \, \text{cm}$ and $DC = 8 \, \text{cm}$ .

DC = 8 , AB=4