Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm.

Given: AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm

To Find: Area of the quadrilateral

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Area of a right-angled triangle

Diagram:

Explanation:

AB² + BC² = AC²

ABC = 90˚

Therefore, Δ ABC is a right-angled triangle.

∴ Area of Δ ABC = (AB × BC) = 1/2 × 3 × 4 cm² = 6 cm²

Let 2s be the perimeter of Δ ACD and a = A C = 5 cm, b = CD = 4 cm and c = AD = 5 cm

∴ 2s = a + b+ c 2s = 5 + 4 + 5 s = 7

∴

= 2√21 cm²

∴ Area of quadrilateral ABCD = (6 + 2√21) cm²

Hence, the area of quadrilateral is (6 + 2√21) cm².