Side of sq =2r =14
Area of sq =142=196 cm2
Area of circ =πr2 =722×7×7=154 cm2
Area of shaded region =Area of sq−Area of circle =196−154=42 cm2.
(area, square, circle, radius, shaded region)
Get the complete, step-by-step math solution for: "Side of sq = 2r = 14 Area of sq = 14² = 196 cm² Area of circ = π r² = {22}{ {7}} × {7} × 7 = 154 cm² Area of shaded region = Area of sq - Area of circ...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Determine the radius of the inscribed circle
When a circle is inscribed in a square, the diameter of the circle is equal to the side of the square. Therefore, the radius of the circle is half the side of the square. Given that the side of the square is 14 cm, we can calculate the radius.
Step 2: Calculate the area of the square
The area of a square is calculated by squaring the length of its side. Given the side of the square is 14 cm, we can find its area.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2, where r is the radius. We will use the value of π=722 for this calculation.
Step 4: Calculate the area of the shaded region
The shaded region is the area of the square that is not covered by the circle. Therefore, we subtract the area of the circle from the area of the square to find the area of the shaded region.