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Question

An isosceles trapezoid ABCD has bases AD=17 cm, BC=5 cm, and side AB=10 cm. Through the vertex B there is a line, which bisects diagonal AC and intersects AD at point M. What is the area of a triangle BDM?    

Answer 1

From BRAINLY DOT COM:

Let E be the midpoint of AC. Then ΔBCE is congruent to ΔMAE, and MA = BC = 5 cm. Then MD = 17 cm -5 cm = 12 cm.

The height of the trapezoid is found from the Pythagorean theorem. If the center 5 cm of the trapezoid is removed, the remaining ends form an isosceles triangle with sides 10 cm and base 17 -5 = 12 cm. Its height in cm is..

h = √(10² -(12/2)²) = √(100 -36) = 8

So ΔBDM has base 12 cm and height 8 cm. its area is.. A = (1/2)(12 cm)(8 cm) = 48 cm²