The bases of an isosceles trapezoid are 5cm and 15cm, and the side edge is 13cm. Find the area of the trapezoid.

Let us draw the height of CH from the top of the obtuse angle C of the trapezoid.

In a rectangular trapezoid, the height drawn from the top of an obtuse angle divides the larger base into two segments, the smaller of which is equal to the half-difference of the bases of the trapezoid, and the larger one – half the sum of the bases.

Then the segment DH = (AD – BC) / 2 = (15 – 5) / 2 = 5 cm.

From the right-angled triangle СDН, according to the Pythagorean theorem, we define the leg СН.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

CH = √144 = 12 cm.

Determine the area of the trapezoid.

S = (AD + BC) * CH / 2 = (15 + 5) * 12/2 = 120 cm2.

Answer: The area of the trapezoid is 120 cm2.