The area of a rectangular trapezoid is 140 cm, and its height is 7. Find the sides of the trapezoid

The area of a rectangular trapezoid is 140 cm, and its height is 7. Find the sides of the trapezoid if one of the bases is 4 larger than the other.

1. Let’s write down the formula for the area of a trapezoid:
S = (a + b) / 2 * h;
2. Let x be a lesser base, then (x + 4) is a greater base.
Knowing the height and area, we will compose the equation:
(x + x + 4) / 2 * 7 = 140;
x + 2 * 7 = 140;
7x = 140 – 14;
x = 18;
x + 4 = 18 + 4 = 22;
Smaller base – 18 cm;
Larger base = 22 cm;
3. Let’s lower the height, forming a triangle with a side.
By the Pythagorean theorem, we find the lateral side:
b = √65 (cm);
4. The other side is equal to the height.
Answer: 18 cm, 22 cm, 7 cm, √65 cm.