# 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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