In a rectangular trapezoid, the smaller base is 6 cm, the smaller side is 5 cm

In a rectangular trapezoid, the smaller base is 6 cm, the smaller side is 5 cm, and the larger side is 13 cm. How to find the area of the trapezoid?

Let us draw from the vertex C the height CH, the length of which is equal to the lateral side AB. Quadrangle ABCH is a rectangle, therefore AH = BC = 6 cm.

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

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

DН = 12 cm.

Then AD = AH + DH = 6 + 12 = 18 cm.

Let’s define the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (6 + 18) * 5/2 = 60 cm2.

Answer: The area of the trapezoid is 60 cm2.