Trapezoid - How to Find the Area Using the Formula

Area of a Trapezoid - How it Works - Video

Example 1

Example 1:

To find the area of a trapezoid, let's use the trapezoid formula ==> (1/2) * (b₁ + b₂) * h; where b₁ is base 1; b₂ is base 2; h is the height. In this example base 1 is 5 cm; base 2 is 9 cm; the height is 7 cm.

Let's use the formula (1/2) * (b₁ + b₂) * h

• (1/2) * (5 + 9) * 7 We substitute the measurements in the formula.

• (1/2) * (14) * 7 We add the bases.

• 7 * 7 We multiply (1/2) and 14.

• 49 cm² We multiply 7 and 7.

So 49 cm² is our final answer.

Example 1 continued:

Why are we multiplying by (1/2)? Well, if we double the original trapezoid and put the two images together, it forms a parallelogram. The area of a parallelogram is Base * Height. In this case our base for the parallelogram is the the total of base 1 + base 2 ==> 9 + 5 ==> 14. Then we can multiply our base, 14, and our height, 7, ==> 14 * 7 ==> 98 cm². Now we can divide the parallelogram in half since we put two together ==> 98 cm² / 2 ==> 49 cm².

Example 2

Example 2:

To find the area of a trapezoid, let's use the trapezoid formula ==> (1/2) * (b₁ + b₂) * h; where b₁ is base 1; b₂ is base 2; h is the height. In this example base 1 is 4 cm; base 2 is 10 cm; the height is 10 cm.

Let's use the formula (1/2) * (b₁ + b₂) * h

• (1/2) * (4 + 10) * 7 We substitute the measurements in the formula.

• (1/2) * (14) * 7 We add the bases.

• 7 * 6 We multiply (1/2) and 14.

• 42 cm² We multiply 7 and 7.

So 42 cm² is our final answer.

Example 2 continued:

Why are we multiplying by (1/2)? Well, if we double the original trapezoid and put the two images together, it forms a parallelogram or in this case a rectangle. The area of a parallelogram is Base * Height. In this case our base for the parallelogram is the the total of base 1 + base 2 ==> 4 + 10 ==> 14. Then we can multiply our base, 14, and our height, 6, ==> 14 * 6 ==> 84 cm². Now we can divide the parallelogram in half since we put two together ==> 84 cm² / 2 ==> 42 cm².

Live Worksheet

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