Find the area of an isosceles trapezoid MKPT if the length of its height MA is 8, and point A

Find the area of an isosceles trapezoid MKPT if the length of its height MA is 8, and point A divides the larger base of the KP into segments, the length of the larger of which is 11.

Let’s construct the MA height of the MKPT trapezoid.

Since the trapezoid is isosceles, the MA height divides the base into two segments, the length of the larger of which is equal to half the sum of the lengths of the bases of the trapezoid.

AР = (MT + KР) / 2 = 11 cm.

Since the middle line of the trapezoid is also equal to the half-sum of the lengths of the bases of the trapezoid, the area of the trapezoid is: Smcr = AР * MA = 11 * 8 = 88 cm2.

Answer: The area of the trapezoid is 88 cm2.