The base of the trapezoid is 4 and 10, and the sides are 5. Find the area of the trapezoid.

Let’s build the height BH.

Since the trapezoid is isosceles, the height BH divides the base of AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases.

AH = (BP – BC) / 2 = (10 – 4) / 2 = 3 cm.

From the right-angled triangle ABN, according to the Pythagorean theorem, we determine the length of the leg BN.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.

BH = 4 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * BH / 2 = (4 + 10) * 4/2 = 28 cm2.

Answer: The area of the trapezoid is 28 cm2.



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