Question

Find the area of the quadrilateral ABCD in which ab=5cm,bc=4.5cm,cd=3.5cm,da=4cm and ac=6.5cm​

Answer 1

A(ABCD) ≈ 17.285 cm²

Explanation:

• Heron formula

A = √s(s - a)(s - b)(s - c)

s = (a + b + c)/2

a ; b ; c = the sides of the triangle

• A(ABCD) = A(ABC) + A(ACD)

1. A(ABC) = √s(s - AB)(s - BC)(s - AC)

s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm

A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)

= √8×3×3.5×1.5

= √126

≈ 11.225 cm²

2. A(ACD) = √s(s - AC)(s - CD)(s - AD)

s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm

A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)

= √7×0.5×3.5×3

= √36.75

≈ 6.060 cm²

3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²