The red color

Geometry Level 1

A square is inscribed in a circle of radius $3$ as shown. What is the area of the red region? Give your answer correct to two decimal places. For the approximation of $\pi$ , use $3.1416$ .

The answer is 10.27.

1 solution

A Former Brilliant Member
Jan 19, 2018

Relevant wiki: Inscribed Squares

Let $x$ be the side length of the square. Then by pythagorean theorem , we have

$6^2 = x^2+x^2$ $\color{#D61F06}\implies$ $36=2x^2$ $\color{#D61F06}\implies$ $18=x^2$

Then the area of the red region is,

$A = \pi r^2 - x^2 = 3.1416(9) - 18 \approx \boxed{10.27~\text{square units}}$

You do not need to specify the value of $\pi$ to be used. If the answer is within $2$ percent of the value you give, it will be considered correct by the program.

Marta Reece - 3 years, 4 months ago

The red color

The answer is 10.27.

1 solution

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