Question

What is the area of the circle shown in the illustration below?

A. 3.14 square centimeters
B. 6.28 square centimeters
C. 9.42 square centimeters
D. 12.56 square centimeters

Answer 1

Easy,

now it looks tricky but it's not,

you're trying to find the Area of the circle, but you don't have the radius.

What you do have is a triangle with two sides labeled
`√(2)`

Now, using Pythagorean Theorem:


`a ^(2)+ b^(2)= c^(2)`


`√(2) ^(2) + √(2) ^(2)= c^(2)`

But we know that the OPPOSITE of square root is squared.

Making it,

2+2=
`c^(2)`

4=
`c^(2)`

2=c

The third side is 2. (Diameter) As the radius, 1.

Now, to find the Area of a Circle,

A=
`\pi`
`r^(2)`

A=
`\pi *1`

Making your answer, 3.14 sq cm, A.

Answer 2

A.) 3.14 sq. cm.

Right triangle. Use Pythagorean theorem to solve for the hypotenuse.

a² + b² = c²
(√2)² + (√2)² = c²
2 + 2 = c²
4 = c²
√4 = √c²
2 = c

The hypotenuse is also the diameter of the circle.

Area of a circle = π r²

radius is 1/2 of the diameter.

A = 3.14 * (1cm)²
A = 3.14 * 1cm²
A = 3.14 cm²