Explanation:
The formula for the area of a triangle is ½ base × height. If we cut a trapezoid along its diagonal, we get two triangles and a rectangle. The two triangles are congruent, and each has a base equal to one of the parallel sides of the trapezoid and a height equal to the distance between the two parallel sides. The area of each triangle is therefore ½ base × height. The rectangle has a base equal to the length of the diagonal and a height equal to the height of the trapezoid. The area of the rectangle is base × height. Adding the areas of the two congruent triangles and the rectangle gives:
Area of trapezoid = ½ (b1 + b2) × h
where b1 and b2 are the lengths of the parallel sides, and h is the height of the trapezoid.