Question

A $1 \times 2$ rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?

$\dfrac{\pi}{2}$

$\dfrac{2\pi}{3}$

$\pi$

$\dfrac{4\pi}{3}$

$\dfrac{5\pi}{3}$

Answer: C

Concepts:Pythagorean Theorem circle area

Difficulty rating: 1370

Video solution:

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Written solution:

Using the Pythagorean theorem, we get that the radius of the semicircle is $\sqrt{2}.$ This means that the area of the semicircle is $\dfrac{1}{2} \cdot \pi \cdot \sqrt{2}^2 = \pi.$ Thus, C is the correct answer.

2013 AMC 8 Problem 20

Answer: C

Difficulty rating: 1370

Video solution:

Written solution:

Problem 20 in Other Years