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In the figure below, the grid consists of unit squares. What is

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In the figure below, the grid consists of unit squares. What is  [#permalink]

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New post 05 Jun 2017, 08:40
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In the figure below, the grid consists of unit squares. What is the area of the polygon?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 15

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Re: In the figure below, the grid consists of unit squares. What is  [#permalink]

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New post 05 Jun 2017, 08:59
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The figure consists of
a square with side 2,
a triangle1 with height=base=2,
and a triangle2 with a height=2 and base=1.

The combined area
= Area of Square(2*2) + Area of triangle1(\(\frac{1}{2}*2*2\)) + Area of triangle2(\(\frac{1}{2}*2*1\))
= 4+2+1 = 7(Option A)
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Re: In the figure below, the grid consists of unit squares. What is  [#permalink]

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New post 05 Jun 2017, 09:03
1
SajjadAhmad wrote:
In the figure below, the grid consists of unit squares. What is the area of the polygon?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 15

Nova GMAT



Nice question:

We can see that the figure is a trapezoidal.

hence the formula will be : 1/2*(sum of parallel sides)*(distance between the parallel sides).

Since the square are unit squares.

Hence,

Area = 1/2*(2+5)*2 = 7

Answer is A

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Re: In the figure below, the grid consists of unit squares. What is  [#permalink]

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New post 05 Jun 2017, 16:44
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Top Contributor
SajjadAhmad wrote:
In the figure below, the grid consists of unit squares. What is the area of the polygon?

(A) 7
(B) 9
(C) 10
(D) 12
(E) 15

Nova GMAT


The great thing about the "fancy" quadrilaterals (squares, parallelograms, rectangles, rhombuses, AND trapezoids) is that they all have the same area formula.
Area = (base)(height)

In the case of a trapezoid, there are two bases (the two parallel sides are considered the bases).
So, what do we do?
We use the average of the two bases

This figure features a trapezoid.
The bottom base has length 5 and the top base has length 2
So, the average of the two bases = (5+2)/2 = 3.5

So, the area of the figure = (base)(height) = (3.5)(2)
= 7

Answer:

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Re: In the figure below, the grid consists of unit squares. What is  [#permalink]

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New post 06 Jun 2017, 00:13
1
We can also solve this question just by observation:

Notice that their are 5 Complete squares in this area. Their area in total = 1*5 = 5
There are 2 half squares on the left (two right angle triangles) whose area add up to area of 1 square = 1
On the right, there is one right angle triangle (whose base is 1 and height is 2). We can either calculate its area as 1/2 * 1 * 2 OR we can observe carefully that its area would be equal to that of one complete square. Area = 1

So total area = 5+1+1 = 7.

Hence A answer
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Re: In the figure below, the grid consists of unit squares. What is  [#permalink]

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Re: In the figure below, the grid consists of unit squares. What is   [#permalink] 19 Feb 2019, 01:04
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