In an isosceles trapezoid ABCD, the larger base AD is equal to the diagonal.

| May 5, 2021 | education

In an isosceles trapezoid ABCD, the larger base AD is equal to the diagonal. Height BM divided the base AD into segments AM = 6 cm and MD = 9 cm. Find the side and height.

Let’s calculate the length of the larger base. AD = AM + DM = 6 + 9 = 15 cm.

Then, by condition, the diagonal BD = AD = 15 cm.

Triangles ABM and DBM are rectangular, since BM is the height.

From the right-angled triangle DBM, we determine the length of the height of the VM using the Pythagorean theorem.

BM ^ 2 = BD ^ 2 – DM ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.

ВM = 12 cm.

In a right-angled triangle ABM, by the Pythagorean theorem, we determine the length of the lateral side AB.

AB ^ 2 = BM ^ 2 + AM ^ 2 = 12 ^ 2 + 6 ^ 2 = 144 + 36 = 180.

AB = 6 * √5 cm.

Answer: The height of the trapezoid is 12 cm, the side is 6 * √5 cm.



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