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?
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Was really easy.
Yeah. I just wrote a long-ish solution because I was bored.
yeah same idea
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
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
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.
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.
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
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
area of square=4 and area of 2 semicircles =22/7 therefore, area of shaded region=4-22/7=0.86
(2x2) - (∏) = 4-3.14 = 0.86
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
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.
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
Simple area of square of side 2 minus 2* area of semi circle
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.)
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.
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First, let's find the area of the square. This is simply 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
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 = π
Looking back at our battle plan, now we just substitute, which produces 4 − π ≈ 0 . 8 6 .