Question

Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]

a) 1/2(AC * BD)
b) 1/2(AB * CD)
c) 1/2(BC * AD)
d) 1/2(AB * CD + BC * AD)

Answer 1

To find the area of quadrilateral ABCD, use the formula for the area of a triangle. The area of quadrilateral ABCD is 1/2 * AB * BC + 1/2 * AD * CD.

Step-by-step explanation:

To find the area of quadrilateral ABCD, we can use the formula for the area of a triangle.

The diagonal AC divides the quadrilateral into two triangles: triangle ABC and triangle ACD. The area of the quadrilateral is the sum of the areas of these two triangles.

The area of triangle ABC is given by 1/2 * AB * BC, and the area of triangle ACD is given by 1/2 * AD * CD.

Therefore, the area of quadrilateral ABCD is 1/2 * AB * BC + 1/2 * AD * CD, which corresponds to option d) 1/2(AB * CD + BC * AD).