In trapezoid ABCDABCD, the bases of ADAD and BCBC are 10 cm and 8 cm, respectively.
| February 9, 2021 | education
In trapezoid ABCDABCD, the bases of ADAD and BCBC are 10 cm and 8 cm, respectively. The area of triangle ABDABD is 25 cm2. Find the area of the trapezoid.
The area of the triangle ABD is 25 cm². The area of the triangle is equal to half the product of the base and the height: SABD = 1/2 * AD * h.
1/2 * 10 * h = 25.
5h = 25;
h = 25/5 = 5 (cm).
The height of the ADB triangle is equal to the height of the trapezoid.
The area of the trapezoid is equal to the product of the half-sum of the bases and the height:
Str = (a + b) / 2 * h = (8 + 10) / 2 * 5 = 9 * 5 = 45 cm².
Answer: the area of the trapezoid is 45 cm².
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