The bases of the isosceles trapezium are 7 and 13 and the lateral side of the wound is 6, find the area of the trapezium.
| February 24, 2021 | education
From the top B of the trapezoid, we will construct the height ВН.
Since the trapezoid is isosceles, the BH height divides the larger base into two segments, the length of the smaller of which is equal to the half-difference of the lengths of its bases.
AH = (AD – BC) / 2 = (13 – 7) / 2 = 3 cm.
In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the leg BН.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 36 – 9 = 27.
BH = 3 * √3 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВН / 2 = (7 +13) * 3 * √3 / 2 = 30 * √3 cm2.
Answer: The area of the trapezoid is 30 * √3 cm2.
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