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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

What is the area of the circle shown in the illustration below A 314 square centimeters B 628 square centimeters C 942 square centimeters D 1256 square centimet class=

Respuesta :

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 [tex] \sqrt{2} [/tex]

Now, using Pythagorean Theorem:

[tex]a ^{2}+ b^{2}= c^{2} [/tex]

[tex] \sqrt{2} ^{2} + \sqrt{2} ^{2}= c^{2} [/tex]

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

Making it,

2+2=[tex] c^{2} [/tex]

4=[tex] c^{2} [/tex]

2=c

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

Now, to find the Area of a Circle,

A=[tex] \pi [/tex][tex] r^{2} [/tex]

A=[tex] \pi *1[/tex]

Making your answer, 3.14 sq cm, A.



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