The diagonals of a trapezoid are 10 and 24. Find the area of a trapezoid if its midline is 13.
| March 20, 2021 | education
Since, by condition, the middle line of the trapezoid is 13 cm, then 13 = (BC + AD) / 2.
(BC + AD) = 13 * 2 = 26 cm.
From the top of C we draw a segment CH parallel to the diagonal BD, then the segment AH = AD + DH = AD + BC = 26 cm, and the segment CH = BD = 10 cm.
Triangle ABD is rectangular, since the Pythagorean theorem holds. 10 ^ 2 + 24 ^ 2 = 26 ^ 2.
Determine the area of the triangle ABН. Savn = АС * НС / 2 = 10 * 24/2 = 120 cm2.
Let’s draw the height of the trapezoid CM, then the area of the trapezoid is equal to: Savsd = (AD + BC) * CM / 2.
The area of the triangle AСН is equal to: Sasn = AH * CM / 2 = (AD + BC) * CM / 2.
Savsd = Sasn = 120 cm2.
Answer: The area of the trapezoid is 120 cm2.
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