A park is in shape of a parallelogram . find area of park
Answers
The area of the park which is in the shape of a parallelogram is 750√7 m².
Concept used:
- Park is in the shape of a parallelogram. Therefore opposite sides are equal.
- For finding the area of a park (parallelogram) = 2 × area of ∆'s
- For finding the area of a park we need to find the area of a triangle by Heron's formula.
Formula used:
semi perimeter, s = (a + b + c) ÷ 2
Area of the triangle by heron’s formula, A = √[s (s - a) (s - b) (s - c)]
Given:
A park is in the shape of a parallelogram whose adjacent sides are 50 cm, 40 cm and Diagonal 60 cm.
To find:
Area of park
Solution:
Step1: Find the semi perimeter of the triangle:
Let the length of the sides of the ∆ be a = 50 cm, b = 40 cm and c = 60 cm.
Let ‘s’ be the semi perimeter of the triangle.
s = (a + b + c) ÷ 2
s = (50 + 40 + 60) ÷ 2
s = 150 ÷ 2
s = 75 cm
Step 2: Find the area of triangle by using heron’s formula :
Area of the triangle , A = √{s(s - a) (s - b) (s - c)}
A = √[75 × (75 - 50) × (75 - 40) × (75 - 60]
A = √[75 × 25 × 35 × 15]
A = √[(25 × 3) × 25 × (5 × 7) × (3 × 5)]
A = √[(25 × 25) × (3 × 3) (5 × 5) × 7}
A = 25 × 3 × 5 √7
A = 375√7 m²
Area of the triangle, A = 375√7 m²
Area of parallelogram = 2 × area of ∆
Area of parallelogram = 2 × 375√7
Area of parallelogram = 750√7 m²
Hence the area of the park is 750√7 m².
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