Find the perimeter and area of the shaded por | vedclass

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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.

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