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

July 24, 2021 | education

| 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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.