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What is the area of shaded region in the figure shown?

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Bunuel
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What is the area of shaded region in the figure shown? [#permalink] New post  27 Oct 2021, 07:15
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What is the area of shaded region in the figure shown?

A. 4/3
B. 8/3
C. 4
D. 8
E. 12


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chetan2u
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What is the area of shaded region in the figure shown? [#permalink] New post  27 Oct 2021, 12:26
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Bunuel wrote:
What is the area of shaded region in the figure shown?

A. 4/3
B. 8/3
C. 4
D. 8
E. 12



y=4 means that this line is parallel to x axis. Therefore, \(\triangle OPQ\) is similar to \(\triangle RSQ\) as shown in the sketch attached.

Similar triangles have areas in the ratio of square of their sides. ratio of areas of \(\triangle OPQ\):\(\triangle RSQ\)=\(OQ^2:SQ^2=1^2:3^2=1:9\)

Area of \(\triangle OPQ\) = \(\frac{1}{2}*\frac{8}{3}*1=\frac{4}{3}\)
Area of \(\triangle RSQ\) = 9* Area of \(\triangle OPQ\) = \(9*\frac{4}{3}\) = \(12\)


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Suhasi
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What is the area of shaded region in the figure shown? [#permalink] New post  12 Nov 2021, 04:02
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We know 2 points on the line - (-8/3,0) and (0,1)

Equation of the line:\( y = mx + b\)

m = 1- 0/0 - (-8/3)
m = \(\frac{3}{8}\)

It is clear from the diagram that b = 1.

So, y = 3x/8 + 1

When y = 4,
4 = 3x/8 + 1
32 = 3x + 8
x = 8

The coordinates of the point on the right hand side are (8,4)

Now we know 2 coordinates of the triangle. The base and the height will measure 3 and 8.
Therefore, area of triangle = \(\frac{1}{2} * b * h\)
= \(\frac{1}{2} * 3 * 8\)
= 12
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bv8562
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Re: What is the area of shaded region in the figure shown? [#permalink] New post  13 Nov 2021, 06:25
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Area of triangle ABC = 1/2*AB*AC

Slope of line L = 3/8

also, 3/8 = 3/x => x = 8

Therefore, AB = 3 units & AC = 8 units

Area = 12 units (E)
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Paras96
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Re: What is the area of shaded region in the figure shown? [#permalink] New post  08 Aug 2023, 23:37
Let △ABC be the triangle whose area we have to calculate, Let B denote (0,1) A denote (0,4) and C denote (x,4)

We can give area of △ABC = base x height/2 = (4-1)(x-0)/2=3x/2

Now to calculate x, we can use another triangle that has coordinates (-8/3,0) (0,0) (0,1)

According to the similar triangle
=> (8/3)/1 = (x)/(4-1)
=>8/3=x/3
=>x=8

Therefore ,
area of △ABC =3x/2 = 3*8/2=12 squnits

Hence E
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Re: What is the area of shaded region in the figure shown? [#permalink]
08 Aug 2023, 23:37
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