2 semicircles cramped in a box

Geometry Level 1

The shaded region is bounded by two semicircles and two sides of a square. If the length of one side is 2, what is the area of the shaded region?

0.31 0.86 0.14 0.69

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

14 solutions

Discussions for this problem are now closed

Finn Hulse
Jun 9, 2014

First, let's find the area of the square. This is simply 2 2 = 4 2^2=4 . Here's what I do on tests: I make a plan of what I'm going to add and subtract and do whatever with and THEN plug in the actual areas:

SHADED AREA = SQUARE BOTH SEMICIRCLES \text{SHADED AREA}=\text{SQUARE}-\text{BOTH SEMICIRCLES}

Notice how the two semicircles can be added up to make a circle. Since it has the same diameter as the side of the square, it's radius is simply one. Plugging this into the formula for the area of a circle,

A = π r 2 A=\pi r^2

A = π A=\pi

Looking back at our battle plan, now we just substitute, which produces 4 π 0.86 4-\pi\approx\boxed{0.86} .

Was really easy.

Rhishikesh Dongre - 7 years ago

Yeah. I just wrote a long-ish solution because I was bored.

Finn Hulse - 7 years ago

yeah same idea

Muhammad Saleem - 7 years ago

Found the question in a PSAT book my brother gave me, I was flipping through the questions looking for good questions. Found nothing completely amazing as you can see

Robert Fritz - 7 years ago
Nisha P Mathew
Jun 19, 2014

Area of the square = 2^2 Area of the semicircles = (πr^2)/2×2 = π (where r = 1) ∴ area of the shaded region = 4 -π = 0.86

Juan Almenara
Jun 13, 2014

El área de un cuadrado de lado 2 es = 2 x 2 = 4 y la de 2 semicírculos es = pi x 1x1 = pi. Restamos: 4 - 3.14 (aproximadamente) = 0.86 (aproximadamente)

Los semicírculos de diámetro 2.

Juan Almenara - 6 years, 12 months ago
Sam Cheung
Jun 10, 2014

Two semicircles make a whole. The square has side length of 2, so area of 4. The semicircles have a radius of 1, the area of the whole circle is Pi. The answer is 4-Pi. I entered 0.858 which is this rounded to 3s.f.

Mayur Gohil
Jun 12, 2014

see this is a box which is a square. and these are two semi circles...so if u are good at analyzing the diagram little more carefully you will see that the problem is showing that the circle is inscribed in square........so area of square -area of circle is the answer.....that is 4 - (3.14)=0.86

Kartik Ramaswamy
Jun 12, 2014

Area of square = 4

Area of 2 semi circles = 2×1/2×3.14×(1)^2 =3.14

Hence shaded region = Area of square - Area of 2 semi circles

= 4 - 3.14 =0.86

Purvi Singh
Jun 12, 2014

area of square=4 and area of 2 semicircles =22/7 therefore, area of shaded region=4-22/7=0.86

Mohamed Elgammal
Jun 12, 2014

(2x2) - (∏) = 4-3.14 = 0.86

S W
Jun 11, 2014

area of sqaure=2 2=4, area of circle=pi r2 =3.14 => 4-3.14=.86

Yes that is my answer too K.KJ.GARG.India

Krishna Garg - 7 years ago
Brian Lee
Jun 11, 2014

Two semicircles = a circle, radius = 1 since the diameter (square side) is 2, so area of square minus the area of the circle [(2x2)-(pi*1)] is the area of the shaded section.

Ali Hassan
Jun 11, 2014

Shaded Area=Area of Square-(Area of Semi-Circle * 2) Shaded Area=(LxW) - ((π r2)/2 * 2) Shaded Area=(2x2) - (3.14 x 1x1) Shaded Area=4 - 3.14 Shaded Area=0.86

Punithan Mech
Jun 10, 2014

Simple area of square of side 2 minus 2* area of semi circle

Fares Salem
Jun 10, 2014

the area of the square = 2 2= 4 square units and the area of the semi circle = {pi r^2}/2 = [pi 1^2]/2 = pi/2 therefore the are of the two semi circles = [pi/2] 2 = pi therefore the area of the shaded part = 4 - pi = 0.86 (approx.)

Robert Fritz
Jun 9, 2014

The whole area of the square is obviously 4. Then since the area of 1 semicircle is 1/2pi R*2 there are 2 of them making the area 4-pi because the radius of 1 semicircle is 1 already.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...