A circular plate has circumference 16.3 inches. What is the area of this plate?

Circumference:  C = 2πr = 16.3

2(3.14)r = 16.3

r = 16.3/6.28

r = 2.5955414

Area:  A = πr2

A = 3.14(2.5955414)2

A = 21.15366242 in2

Rounded to nearest whole number the area is 21 in2

Step-by-step explanation:

* Lets revise some rules of a circle

- The circumference of a circle = 2πr , where r is the radius of it

- The area of the circle = πr²

* Lets solve the problem

∵ A circular plate has circumference 16.3 inches

∵ The circumference = 2πr

∵ π = 3.14

- Lets find the radius of the plate

∵ 16.3 = 2(3.14)r

∴ 16.3 = 6.28r

- Divide both sides by 6.28

∴ r = 16.3/6.28 = 2.5955 ≅ 2.6

∴ The radius of the plate is 2.6 inches

* Lets find the area of the plate

∵ The area = πr²

∵ π = 3.14

∵ 4 = 2.6

∴ The area = 3.14(2.6)² = 21.22 ≅ 21

* The area of the plate is 21 inches

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240