In an isosceles trapezoid, the large base is 44 m, the lateral side is 17 m, the diagonal is 39 m. Find the area of the trapezoid.
September 14, 2021 | education
| 1. Let’s designate the vertices of the trapezoid ABCD. Bases BC and AD. CH height.
2. According to Heron’s formula, we calculate the area S of the triangle ACD:
S = √50 (50 – 44) (50 – 39) (50 – 17) = √108900 = 330 cm ^ 2.
3. We calculate the length of the CH using a different area formula:
S = CH x AD / 2; CH = 2 x S / 44 = 660/44 = 15 cm.
4. The length of the segment AH = √AC ^ 2 – CH ^ 2 = √39 ^ 2 – 15 ^ 2 = √1296 = 36 cm.
4. According to the properties of an isosceles trapezoid AH = (BC + AD) / 2.
5. Area of the trapezoid: AH x CH = 36 x 15 = 540 cm ^ 2.
Answer: the area of the trapezoid is 540 cm ^ 2.
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