Question

I have a challenge for someone: What is the area of the shaded area if the perimeter is 68 (fake answers will be reported)

Answer 1

126.14in²

Explanation:

P = 2w + 2l

68 = 2(x + 2) + 2(20)

68 = 2x + 4 + 40

68 = 2x + 44

24 = 2x

12 = x

x + 2

12 + 2

14 (width)

14 * 20

280in² (area of rectangle)

A = πr²

A = π(7)²

A = 49π

A = 153.86 (area of circle)

280 - 153.86

126.14 (area of shaded region)

Best of Luck!

Answer 2

• 126.14 in²

Explanation:

Given

• Rectangle with sides of 20 in and x+2 in and perimeter of 68 in

Perimeter = 2(l + w)

• l = 20 in, w = x + 2 in, P = 68 in

Substitute values in perimeter formula

• 68 = 2(20 + x + 2)
• 34 = x + 22
• x = 34 - 22
• x = 12 in

Then, the value of width is

• w = 12 + 2 = 14 in

Area of rectangle

• A = lw = 20*14 = 280 in²

Area of circle

• A = πr² = 3.14*7² = 153.86

Shaded area

• 280 - 153.86 = 126.14 in²