In trapezoid ABCD, angle A is equal to angle B equal to 90 gradients. AB = 8 cm BC = 4 cm CD = 10 cm find

| August 12, 2021 | education

In trapezoid ABCD, angle A is equal to angle B equal to 90 gradients. AB = 8 cm BC = 4 cm CD = 10 cm find a) the area of the triangle ACD b) the area of the trapezoid ABCD

Let us draw from point C of the trapezoid the height CH, which is equal to the length AB of the lateral side of the trapezoid CH = AB = 8 cm.

The area of the trapezoid can be found by adding the areas of the rectangle ABCH and the triangle CHD.

Savsn = AB * BC = 8 * 4 = 32 cm2.

Ssnd = (CH * HD) / 2.

НD is found by the Pythagorean theorem.

НD ^ 2 = СD ^ 2 – CH ^ 2 = 100 – 64 = 36.

НD = 6 cm.

Then Ssnd = (8 * 6) / 2 = 24 cm2.

Find the area of the trapezoid.

Savsd = Ssnd + Savsn = 24 + 32 = 56 cm2.

Find the area of the triangle ACD.

Sasd = (АD * СН) / 2 = ((АН + НD) * СН) / 2 = ((4 + 6) * 8) / 2 = 40 cm2.

Answer: Sax = 40 cm2, Savd = 56 cm2.



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