Question

Find the area of the trapezoid and the area of the kite.

a.

A trapezoid with bases of length 20 and 12 centimeters, and height of 8 centimeters. The distance from where the perpendicular height intersects the longer base to the corner is 4 centimeters.
b.

A kite with end to end length of 10 inches. The short diagonal is 6 inches. The long diagonal is split by the other diagonal into two parts, one 4 inches, the other 6 inches.

Answer 1

a) Trapezoid area = (average of bases) × height = ((20 + 12)/2) × 8 = 16 × 8 = 128 cm².

(The extra distance along the base is not needed for the area.)

b) For a kite the area = (d1 × d2)/2. Here the diagonals are 10 in and 6 in, so area = (10 × 6)/2 = 30 in².