Question

Find the area of quadrilateral abcd, where a b is equal to 7 cm, d a is equal to 15 cm, ac is equal to 9 cm bc is equal to 6 cm and cd is equal to 12 cm

Answer 1

Answer:

Area of ABCD = 331.88 cm²

Step-by-step explanation:

See the attachment for the figure.

Area of triangle ABC by Heron's formula = √s(s-a)(s-b)(s-c), where a, b and c are the three sides of the triangle and s = (a+b+c)/2 = (7+6+9)/2 = 22.

Thus, area of triangle ABC = √22(22-7)(22-9)(22-6) = √22(15)(13)(18) = √2*11*3*5*13*2*3*3 = 2*3*√11*5*13*3 = 6√2145 cm²

Similarly, Area of triangle ADC = √18(18-15)(18-12)(18-9) = √18*3*6*9 = √3*3*2*3*3*2*3*3 = 3*3*3*2 = 54 cm²

Thus, Area of Quadrilateral ABCD = 6√2145 cm² + 54 cm² = (277.88+54) cm² = 331.88 cm²