find the area of the shaded region
Answers
area of big square = 14*14 = 196 cm*cm
area of all small semi-circles = 2 *(2*3.14*1) = 12.56 cm*cm
area of middile square = 2*2 = 4cm*cm
total area of unshaded region = 16.5
area of shaded region = 196-16.5 = 179.5 cm*cm
The Area of Shaded Region Can be Found by Subtracting the Area of Flower from the Area of Big Square.
We can Notice that the Side of the Square is 14cm and The Flower is Made of Four Semi-Circles or Two Complete Circles and a Small Square inside.
3cm + Radius of Semi Circle + Side of Small Square + Radius of Semi Circle + 3cm = 14cm
⇒ 2 × (Radius of Semi-Circle) + Side of Small Square = 8cm
The Lengths which satisfy the above Equation are :
Radius of Semi-Circle = 2cm and Side of Small Square = 4cm
Area of the Flower = Area of 4 Semi Circles or Two Circles + Area of Square
We know that Area of Circle is given by : πr²
⇒ Area of 4 Semi - Circles or 2 Circles = 2 × (π × 2²) = 8π = 25.132 cm²
We know that Area of Square is given by : Side × Side
⇒ Area of Small Square = 4 × 4 = 16 cm²
⇒ Area of Big Square = 14 × 14 = 196 cm²
⇒ Area of Flower = (25.132 + 16) = 41.132 cm²
⇒ Area of Shaded Region = Area of Big Square - Area of Flower
⇒ Area of Shaded Region = (196 - 41.132) = 154.86 cm²