In an isosceles trapezoid ABCD, the large base AD is equal to the diagonal. Height BM splits the base AD
| August 13, 2021 | education
In an isosceles trapezoid ABCD, the large base AD is equal to the diagonal. Height BM splits the base AD into segments AM = 6cm MD = 9cm. Find the side and height.
Determine the length of the base AD. AD = AM + DM = 6 + 9 = 15 cm.
By condition, BD = AD, then BD = 15 cm.
Determine the length of the leg BM, using the Pythagorean theorem, in the triangle BDM.
BM ^ 2 = BD ^ 2 – DM ^ 2 = 225 – 81 = 144.
BM = 12 cm.
In a right-angled triangle ABM, we also use the Pythagorean theorem to determine the hypotenuse AB.
AB ^ 2 = BM ^ 2 + AM ^ 2 = 144 + 36 = 180.
AB = 6 * √5 cm.
Answer: The side of the trapezoid is 6 * √5 cm, the height of the trapezoid is 12 cm.
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