The lengths of the sides of the trapezoid are 20 and 34, and the lengths of the bases are 18 and 60.

| May 18, 2021 | education

The lengths of the sides of the trapezoid are 20 and 34, and the lengths of the bases are 18 and 60. Find the area of the trapezoid.

1. Vertices of the trapezoid A, B, C, D. AB = 20 units of measurement, CD = 34 units of measurement. BC = 18 units. AD = 60 units.

2. Draw the heights BE and SK to the base AD. BE = SK.

3. AE + DK = 60 – 18 = 42 units.

4. Let us denote the lengths of the segment AE by x. The length of the segment is DK = (42 – x).

5. BE² = AB² – AE² = 400 – x².

CK² = CD² – DK² = 34² – (42 – x) ² = 1156 – 1764 + 84x – x².

6. We equate the right-hand sides of these expressions:

400 – x² = 1156 – 1764 + 84x – x².

84x = 1008.

x = 12.

AE = 12 units of measurement.

7. We calculate the length of the height BE:

BE = √AB² – AE² = √20² -12² = √400 – 144 = √256 = 16 units.

8. Calculate the area (S) of the trapezoid:

S = (BC + AD) / 2 x BE = (18 + 60) / 2 x 16 = 624 units of measure².

Answer: the area of ​​a given trapezoid is 624 units of measurement².



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