Question

ABCD is a quadrilateral with ab =5 cm bc=4 cm cd=5cm and da=6cm.if the diagonal ac=7cm find area of quadrilateral ​

Answer 1

Answer:

24.4 cm²

Step-by-step explanation:

The diagonal AC divides the quadrilateral into 2 triangles, namely Δ ABC and Δ ACD.

Area of Δ ABC

Using Heron's formula,

s = (a + b + c) / 2

  = (5 + 4 + 7) / 2

  = 8

Area = √s(s-a)(s-b)(s-c)

        = √8(8-5)(8-4)(8-7)

        = √8 × 3 × 4 × 1

        = √2^5 × 3

        = 4√6 cm²

Area of Δ ACD

Using Heron's formula,

s = (a + b + c) / 2

  = (5 + 6 + 7) / 2

  = 9

Area = √s(s-a)(s-b)(s-c)

        = √9(9-5)(9-6)(9-7)

        = √9 × 4 × 3 × 2

        = √2³ × 3³

        = 6√6 cm²

∴ Total area = 6√6 + 4√6

                    = 10√6

                    = 24.4 cm²

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