Calculate Trapezoid Area: Finding Area of ABCD with Bases 5 and 10

Question

Given the following trapezoid:

AAABBBCCCDDD5104

Calculate the area of the trapezoid ABCD.

Video Solution

Solution Steps

00:00 Calculate the area of the trapezoid
00:03 We'll use the formula for calculating trapezoid area
00:07 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2
00:16 Let's substitute appropriate values and solve for the area
00:27 Let's factor 4 and simplify
00:38 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll calculate the area of trapezoid ABCD using the appropriate formula.

The formula for the area A A of a trapezoid is given by:

A=12×(Base1+Base2)×Height A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

Substituting the given values into the formula, we have:

A=12×(5+10)×4 A = \frac{1}{2} \times (5 + 10) \times 4

First, calculate the sum of the bases:

5+10=15 5 + 10 = 15

Multiply by the height, and then take half:

A=12×15×4=12×60=30 A = \frac{1}{2} \times 15 \times 4 = \frac{1}{2} \times 60 = 30

Therefore, the area of the trapezoid ABCD is 30 square units.

Answer

30