The bases of the isosceles trapezoid are 10 and 18, and the lateral side is 5. Find the area of the trapezoid.
| April 9, 2021 | education
From the top B we construct the height BH to the base of AD. Since the trapezoid ABCD is isosceles, its height BH divides the larger base into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid.
AH = (AD – BC) / 2 = (18 – 10) / 2 = 8/2 = 4 cm.
The ABN triangle is rectangular, then, according to the Pythagorean theorem, we determine the length of the BH leg.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.
BH = 3 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВН / 2 = (10 + 18) * 3/2 = 42 cm2.
Answer: The area of the trapezoid is 42 cm2.
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