Find the perimeter and area of the shaded por | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Area of the shaded portion = (Area of the rectangle) - (Area of the four sectors).Each sector is a quadrant of a circle with radius $r = 10\, cm$.

Vedclass · Accepted Answer

$90.8\, cm, 414\, cm^2$

Vedclass · Answer

(A) Area of the shaded portion = (Area of the rectangle) - (Area of the four sectors).Each sector is a quadrant of a circle with radius $r = 10\, cm$. The four quadrants together form a full circle of radius $10\, cm$.Area of the rectangle = $28\, cm 	imes 26\, cm = 728\, cm^2$.Area of the circle = $\pi r^2 = 3.1416 	imes (10)^2 = 314.16\, cm^2$.Area of the shaded portion = $728 - 314.16 = 413.84\, cm^2 \approx 414\, cm^2$.Perimeter of the shaded portion = (Sum of the straight edges) + (Sum of the arc lengths of the four sectors).The straight edges are: $(28 - 10 - 10) + (28 - 10 - 10) + (26 - 10 - 10) + (26 - 10 - 10) = 8 + 8 + 6 + 6 = 28\, cm$.The four arcs form a full circle circumference: $2\pi r = 2 	imes 3.1416 	imes 10 = 62.832\, cm$.Total Perimeter = $28 + 62.832 = 90.832\, cm \approx 90.8\, cm$.

Find the perimeter and area of the shaded portion of the adjoining diagram.

Similar Questions

If the area of a square is $50$ $sq$ units,then the area of the circle drawn on its diagonal is

$A$ $2 \text{ m}$ broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is $96 \text{ m}^2$. The rate of construction is $₹ 50 / \text{ m}^2$. Find the total cost of construction (in $₹$).

The perimeters of a circle,a square,and an equilateral triangle are the same,and their areas are $C$,$S$,and $T$ respectively. Which of the following statements is true?

What is the area of the shaded portion if each side of the square measures $21\,cm$? (in $cm^2$)

Length of a rectangle is twice of its breadth. Area of the rectangle is $18 \, m^{2}$. What would be its perimeter? (in $m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module