Question Video: Finding the Area of a Trapezoid | Nagwa Question Video: Finding the Area of a Trapezoid | Nagwa

Question Video: Finding the Area of a Trapezoid Mathematics • Second Year of Preparatory School

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๐ด๐ต๐ถ๐ท is a trapezoid, where line segment ๐ด๐ท โซฝ line segment ๐ต๐ถ, ๐ด๐ท = 22 cm, and ๐ต๐ถ = 13 cm. If the area of โ–ณ๐ด๐ต๐ถ is 65 cmยฒ, what is the area of the trapezoid?

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Video Transcript

๐ด๐ต๐ถ๐ท is a trapezoid, where line segment ๐ด๐ท is parallel to line segment ๐ต๐ถ, ๐ด๐ท equals 22 centimeters, and ๐ต๐ถ equals 13 centimeters. If the area of triangle ๐ด๐ต๐ถ is 65 square centimeters, what is the area of the trapezoid?

Weโ€™ve been given various information about this trapezoid and asked to calculate its area. The area of a trapezoid is equal to half the sum of the lengths of its parallel sides, usually denoted by ๐‘Ž and ๐‘, multiplied by the height, denoted by โ„Ž.

Weโ€™ve been given the lengths of the parallel sides, the line segments ๐ด๐ท and ๐ต๐ถ, which are 22 and 13 centimeters, respectively. But we havenโ€™t been given the trapezoidโ€™s height. Weโ€™ll need to use the other information in the question to calculate this before we can find the trapezoidโ€™s area.

The other information given is that the area of triangle ๐ด๐ต๐ถ is 65 square centimeters. Thatโ€™s this triangle here. Now, the area of a triangle is found using the formula a half multiplied by its base multiplied by its perpendicular height. The base of triangle ๐ด๐ต๐ถ is common with a side of the trapezoid, side ๐ต๐ถ, which is of length 13 centimeters. The height of triangle ๐ด๐ต๐ถ is the same as the height of the trapezoid. And so we can form an equation. 65 is equal to a half multiplied by 13โ„Ž.

We can solve this equation to find the height of the triangle and therefore the height of the trapezoid. Multiplying both sides of the equation by two gives 130 equals 13โ„Ž. And then dividing both sides of the equation by 13 gives โ„Ž equals 10.

Weโ€™ve now found that the height of the trapezoid is 10 centimeters. And so weโ€™re ready to calculate its area. Substituting 13 and 22 for the lengths of the parallel sides and 10 for the height into the formula for the area of a trapezoid gives that the area of the trapezoid ๐ด๐ต๐ถ๐ท is equal to a half multiplied by 13 plus 22 multiplied by 10. 13 plus 22 is 35, and a half multiplied by 10 is five. So the calculation simplifies to five multiplied by 35, which is 175.

By first using the area of triangle ๐ด๐ต๐ถ to calculate the trapezoidโ€™s height, weโ€™ve found that the area of the trapezoid is 175 square centimeters.

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