In trapezoid ABCD, the bases of AD and BC are 6 and 1, respectively, and its area is 42. Find the area of triangle ABC.
| August 27, 2021 | education
The area of the trapezoid is Sabcd = ((AD + BC) / 2) * h, where h is the height of the trapezoid.
From this formula we find the height of the trapezoid.
42 = (6 + 1) / 2 * h.
84 = 7 * h.
h = 12.
The area of the triangle ABC is found by the following formula:
Sabc = Sabcd – Sacd = 42 – ½ * AD * h = 42 – ½ * 6 * 12 = 42 – 36 = 6.
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