Question

The figure is made up of a square and a rectangle. Find the area of the shaded region 16 by 3 by 7

Answer 1

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Answer 2

The area of the shaded region formed by a square with side length 16 units and a rectangle with dimensions 3 by 7 units is 155 square units.

Step-by-step explanation:

To calculate the area of the shaded region, we can find the individual areas of the square and the rectangle, then subtract the area of the rectangle from the area of the square.

The area
`(\(A_s\))` of the square is given by
`\(A_s = s^2\),` where
`\(s\)` is the side length. In this case,
`\(s = 16\), so \(A_s = 16^2 = 256\)` square units.

The area
`(\(A_r\))` of the rectangle is given by
`\(A_r = l * w\),` where
`\(l\)` is the length and
`\(w\)` is the width. Here,
`\(l = 7\) and \(w = 3\), so \(A_r = 7 * 3 = 21\) square units.`

Therefore, the area of the shaded region
`(\(A_{\text{shaded}}\))` is obtained by subtracting the area of the rectangle from the area of the square:

`\[ A_{\text{shaded}} = A_s - A_r = 256 - 21 = 155 \]`square units.

In conclusion, the area of the shaded region is 155 square units, demonstrating the application of basic geometric formulas for squares and rectangles.