Question

A park is in the shape of a quadrilateral ABCD, has ZC = 90°, AB = 9 m, BC = 12 cm, CD
AD = 8 m. The gardener has divided it into two parts by joining BD and has grown red roses
triangular plot BCD and yellow roses in plot ABD. Find the area covered by each colored roses plants?​

Answer 1

Concept Used:-

• we divide the quadrilateral into 2 triangular parts and use Heron’s formula or any other suitable formula to calculate the area of the triangular parts.

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Given:-

• ∠C = 90º,
• AB = 9 m,
• BC = 12 m, CD = 5m
• AD = 8 m.

step-by-step solution:-

• Join the diagonal BD which divides quadrilateral ABCD in two triangles i.e ∆BCD & ∆ABD.

In Δ BCD,

By applying Pythagoras Theorem

⟶ BD²= BC² + CD²

⟶ BD² = 12²+ 5²= 144+25

⟶ BD²= 169

⟶ BD = √169 = 13m

∆BCD is a right angled triangle.

⟶ Area of ΔBCD = 1/2 ×base× height

⟶ 1/2× 5 × 12= 30 m²

For ∆ABD,

Let a = 9m, b = 8m, c = 13m

Now,

Semi perimeter of ΔABD,(s) = (a+b+c) /2

⟶ s = (8 + 9 + 13)/2 m

⟶ 30/2 m = 15 m

⟶ s = 15m

Using heron’s formula,

Area of ∆ABD = √s (s-a) (s-b) (s-c)

⟶ √15(15 – 9) (15 – 9) (15 – 13)

⟶ √15 × 6 × 7× 2

⟶ √5×3×3×2×7×2

⟶ 3×2√35

⟶ 6√35= 6× 5.92

[ √6= 5.92..]

⟶ 35.52m² (approx)

Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD

⟶ 30+ 35.5 = 65.5m²

Hence, area of the park is 65.5m²

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Hope this will help you...!!!