# 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.

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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