What is the area of the given heart shape figure.
please tell of both.
Answers
Answer:
a. Area of the heart shape = 87.465m²
b. Area of the heart shape = 100.0925m²
Step-by-step explanation:
a. Area of the heart shape = area of the square + area of the semicircles
Area of the square = a² = 7² = 49m² (a = side = 7m (given))
Since, the diameter of the semicircles are equal, we can consider their as a circle.
∴ Area of the circle = πr² = 3.14 × (3.5)² = 3.14 × 12.25 = 38.465m²
(radius= diameter / 2 = 7/2 = 3.5m , π = 3.14)
Area of the heart shape = area of the square + area of the semicircles
= 49 + 38.465 = 87.465m²
b. Area of the heart shape = area of the rectangle + area of the semicircles
Area of the rectangle = length × breadth = 9 × 6 = 54m²
Area of the semicircle having the diameter 6m = πr²/2
= (3.14 × 3²)/2 = (3.14 × 9)/2 = 28.26/2 = 14.3m²
(radius = 6/2 = 3m)
Area of the semicircle having the diameter 9m = πr²/2
= 3.14 × (4.5)²/2 = (3.14 × 20.25)/2 = 63.585/2 = 31.7925m²
(radius = 9/2 = 4.5m)
Area of the semicircles = Area of the semicircle having the diameter 6m + Area of the semicircle having the diameter 9m = 14.3 + 31.7925 = 46.0925m²
Area of the heart shape = area of the rectangle + area of the semicircles
= 54 + 46.0925 = 100.0925m²