Question

A quadrilateral with diagonal 8 cm, and heights from opposite vertices to the diagonal are 4 cm and 6 cm respectively, with non-parallel sides 6.5 cm and 10 cm, and height 7.2 cm. The area is:

a) 26 cm^2
b) 36 cm^2
c) 45 cm^2
d) 52 cm^2

Answer 1

The area of the quadrilateral is 59.4 cm².

Step-by-step explanation:

Given a quadrilateral with a diagonal of 8 cm, heights of 4 cm and 6 cm from opposite vertices to the diagonal, non-parallel sides of 6.5 cm and 10 cm, and a height of 7.2 cm, we can find the area of the quadrilateral using the formula for the area of a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides.

The area of a trapezoid is given by the formula:

Area = 0.5 * (sum of the lengths of the parallel sides) * height

In this case, the lengths of the parallel sides are 6.5 cm and 10 cm, and the height is 7.2 cm. Substituting these values into the formula, we get:

Area = 0.5 * (6.5 cm + 10 cm) * 7.2 cm

Area = 0.5 * 16.5 cm * 7.2 cm

Area = 59.4 cm²

Therefore, the area of the quadrilateral is 59.4 cm². None of the provided answer choices match this result, so there may be an error in the given choices.