In an isosceles trapezoid ABCD, the side AB is 13. and the bases are 7 and 31. Find the area of the trapezoid.
| May 10, 2021 | education
From the top of the obtuse angle B, we lower the height BH.
In an isosceles trapezoid, the height drawn from the apex of an obtuse angle divides the larger base into two segments, the smaller of which is equal to the half difference of the base lengths.
AH = (AD – BC) / 2 = (31 – 7) / 2 = 24/2 = 12 cm.
In the right-angled triangle ABN, according to the Pythagorean tower, we determine the length of the leg BH.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.
BH = 5 cm.
Determine the area of the trapezoid.
Savsd = (АD + ВС) * BН / 2 = (31 + 7) * 5/2 = 95 cm2.
Answer: The area of the trapezoid is 95 cm2.
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