Question

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

A. 26.47 units²
B. 28.53 units²
C. 27.28 units²
D. 33.08 units²

Answer 1

B) 28.53 unit²

Explanation:

The diagonal AD divides the quadrilateral in two triangles:

1. Triangle ABD
2. Triangle ACD

Area of Quadrilateral will be equal to the sum of Areas of both triangles.

i.e.

Area of ABCD = Area of ABD + Area of ACD

Area of Triangle ABD:

Area of a triangle is given as:

`Area = (1)/(2) * base * height`

Base = AB = 2.89

Height = AD = 8.6

Using these values, we get:

`Area = (1)/(2) * 2.89 * 8.6 = 12.43`

Thus, Area of Triangle ABD is 12.43 square units

Area of Triangle ACD:

Base = AC = 4.3

Height = CD = 7.58

Using the values in formula of area, we get:

`Area = (1)/(2) * 4.3 * 7.58 = 16.30`

Thus, Area of Triangle ACD is 16.30 square units

Area of Quadrilateral ABCD:

The Area of the quadrilateral will be = 12.43 + 16.30 = 28.73 units²

None of the option gives the exact answer, however, option B gives the closest most answer. So I'll go with option B) 28.53 unit²