In an isosceles trapezoid, the bases are 5 and 23 at the base angle is 45 ° find the area of the trapezoid.
| January 30, 2021 | education
Let us draw the ВН height from the top of the obtuse angle of the trapezoid.
Since the AВСD trapezoid is isosceles, the ВН height cuts off two segments based on the AD, the length of the smaller of which is equal to the half-difference of the lengths of the trapezoid bases.
AH = (AD – BC) / 2 = (23 – 5) / 2 = 18/2 = 9 cm.
In a right-angled triangle ABН, the angle ВAН = 45, then the angle ABН = 180 – 90 – 45 = 45, and therefore the triangle ABН is isosceles, ВН = AH = 9 cm.
Determine the area of the trapezoid.
Savsd = (ВС + AD) * ВН / = (5 + 23) * 9/2 = 126 cm2.
Answer: The area of the trapezoid is 126 cm2.
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