Question

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

Answer 1

Answer:

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Answer 2

Figure:-

Given:-

• AB=3cm,BC=3cm ,CD 4cm , CD= 4cm ,DA=5cm and AC=5cm.

To find:-

• Find the area of a quadrilateral ABCD.

Solutions:-

In ∆ABC,

AC² = AB² + BC²

(5)² = (3)² +(4)²

Therefore,

∆ABC is a right angle triangle at point B.

Area of ∆ABC = 1/2 × AB × BC

= 1/2 × 3 × 4

= 3 × 2

= 6cm

In ∆ADC,

S = perimeter/2

S = (5 + 4 + 5)/2

S = 14/2

S = 7cm

By heroe's formula,

Area of triangle = √s(s - a)(s - b)(s - c)

Area of ∆ADC = √7(7 - 5)(7 - 4)(7 - 5)

= √7 × 2 × 3 × 2

= √84

= 2√21

= 2 × 4.583

= 9.166cm²

Area of ABCD = Area of ∆ABC + Area of ∆ACD

= 6 + 9.166

= 15.166

= 15.2cm²

Hence, the area of a quadrilateral ABCD is 15.2cm²