The diagonal of an isosceles trapezoid is perpendicular to the lateral side.

| September 16, 2021 | education

The diagonal of an isosceles trapezoid is perpendicular to the lateral side. Find the area of the trapezoid if its bases are 7cm and 25cm

1. The tops of the trapezoid A, B, C, D. BC = 7 cm. AD – 25 cm.

2. Let us draw from the top B to the height of the ВН.

3. We calculate the length of the segment AH, which, according to the properties of an isosceles trapezoid, is calculated by the formula:

AH = (AD – BC) / 2 = (25 – 7) / 2 = 9 cm.

4. Calculate the length of the segment DH:

DH = (AD + BC) / 2 = (25 + 7) / 2 = 16 cm.

5. The length of the height BH, drawn from the vertex of the right angle of the triangle ABD, is calculated by the formula:

BH = √AN x DH = √9 x 16 = 12 cm.

6. Calculate the area (S) of the trapezoid ABCD:

S = (ВС + АD) / 2 х ВН = (25 + 7) / 2 х 12 = 192 cm².

Answer: the area of a given trapezoid is 192 cm².



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