Calculate Trapezoid Area: Finding Area with Height 4 and Parallel Sides 6.5 and 10

Question

What is the area of the trapezoid in the figure?

6.56.56.5101010444AAABBBCCCDDDEEE

Video Solution

Solution Steps

00:00 Calculate the area of the trapezoid
00:03 We'll use the formula for calculating the area of a trapezoid
00:07 (Sum of bases(AB+DC) multiplied by height(H))divided by 2
00:14 We'll substitute appropriate values according to the given data and solve to find the area
00:19 In this case, the height is AE
00:33 Divide 4 by 2
00:48 And this is the solution to the problem

Step-by-Step Solution

To solve this problem, we'll compute the area of the trapezoid using the given dimensions and the area formula:

  • Step 1: Identify the given dimensions:
    • Base b1=10 b_1 = 10 cm
    • Base b2=6.5 b_2 = 6.5 cm
    • Height h=4 h = 4 cm
  • Step 2: Use the trapezoid area formula:

    • The formula for the area of a trapezoid is A=12(b1+b2)h A = \frac{1}{2}(b_1 + b_2)h .

  • Step 3: Substitute the given values into the formula:

    • A=12(10+6.5)×4 A = \frac{1}{2}(10 + 6.5) \times 4

  • Step 4: Calculate the area:

    • First, calculate the sum of the bases: 10+6.5=16.5 10 + 6.5 = 16.5 .

    Next, multiply by the height: 16.5×4=66 16.5 \times 4 = 66 .

    Finally, divide by 2 to get the area: 662=33\frac{66}{2} = 33 cm².

Therefore, the area of the trapezoid is 33 33 cm².

Answer

33 33 cm².

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Area of a Trapezoid: Applying the formula