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In the figure above, all streets run in straight lines. If the angle

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In the figure above, all streets run in straight lines. If the angle  [#permalink]

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New post 22 Feb 2018, 20:07
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In the figure above, all streets run in straight lines. If the angle of intersection of Avenue Foche and Victor Hugo Street is 90° and Avenue Foche is parallel to St. Michael's Boulevard, then what is the area of the shaded portion of the figure (expressed in square feet)?

(A) 600

(B) 750

(C) 1350

(D) 2400

(E) 3750

Attachment:
2018-02-23_0806.png
2018-02-23_0806.png [ 58.37 KiB | Viewed 577 times ]

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Re: In the figure above, all streets run in straight lines. If the angle  [#permalink]

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New post 22 Feb 2018, 20:25
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Area of the shaded region is the sum of the area of the rectangle and the area of the right-angled triangle

Area of rectangle = \(20*30 = 600\)
Area of triangle = \(\frac{1}{2}*50*30 = 25*30 = 750\)

Therefore, the area of the shaded region is \(600 + 750 = 1350\)(Option C)
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Re: In the figure above, all streets run in straight lines. If the angle  [#permalink]

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New post 22 Feb 2018, 22:50
We can split the image into 2 areas, one rectangle and one triangle.

Area of rectangle = 30 * 20 = 600
Are of triangle= (50*30)/2 = 750

Adding both = 1350

Ans: C
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Re: In the figure above, all streets run in straight lines. If the angle  [#permalink]

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New post 22 Feb 2018, 23:49
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Bunuel wrote:
Image
In the figure above, all streets run in straight lines. If the angle of intersection of Avenue Foche and Victor Hugo Street is 90° and Avenue Foche is parallel to St. Michael's Boulevard, then what is the area of the shaded portion of the figure (expressed in square feet)?

(A) 600

(B) 750

(C) 1350

(D) 2400

(E) 3750

Attachment:
2018-02-23_0806.png


Area of a trapezoid = (1/2) * (Sum of bases) * height = (1/2)*(20 + 70)*30 = 1350

Answer (C)
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Re: In the figure above, all streets run in straight lines. If the angle  [#permalink]

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New post 23 Feb 2018, 00:48
Bunuel wrote:
Image
In the figure above, all streets run in straight lines. If the angle of intersection of Avenue Foche and Victor Hugo Street is 90° and Avenue Foche is parallel to St. Michael's Boulevard, then what is the area of the shaded portion of the figure (expressed in square feet)?

(A) 600

(B) 750

(C) 1350

(D) 2400

(E) 3750

Attachment:
2018-02-23_0806.png



20x30 = 600

70-20 = 50

h= 30

area of triangle = 1/2 x 30 x 50 = 750

750+600 = 1350

(C) imo
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Re: In the figure above, all streets run in straight lines. If the angle &nbs [#permalink] 23 Feb 2018, 00:48
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