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655-705 (Hard)|   Geometry|      
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georgecambridge
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A garden located on level ground is in the shape of a square region 09 May 2023, 07:37
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A garden located on level ground is in the shape of a square region with two adjoining semicircular regions whose diameters are two opposite sides of the square. The radius of each semicircle is 10 meters. The garden will be surrounded along its edge by a sidewalk with a uniform width of 1.5 meters. What will be the area of the sidewalk, in square meters?

A. 60
B. 80
C. 130
D. 140
E. 160
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georgecambridge
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A garden located on level ground is in the shape of a square region 09 May 2023, 08:20
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Can someone help me visualize the information provided? (at least)
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gmatophobia
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A garden located on level ground is in the shape of a square region 09 May 2023, 08:24
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georgecambridge
A garden located on level ground is in the shape of a square region with two adjoining semicircular regions whose diameters are two opposite sides of the square. The radius of each semicircle is 10 meters. The garden will be surrounded along its edge by a sidewalk with a uniform width of 1.5 meters. What will be the area of the sidewalk, in square meters?

A. 60
B. 80
C. 130
D. 140
E. 160
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Can you indicate the OA georgecambridge
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georgecambridge
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A garden located on level ground is in the shape of a square region 09 May 2023, 10:42
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Sorry don't have official answer
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georgecambridge
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A garden located on level ground is in the shape of a square region 14 May 2023, 08:55
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Can anyone explain it please?
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Flower_Child
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A garden located on level ground is in the shape of a square region 17 May 2023, 10:11
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georgecambridge
A garden located on level ground is in the shape of a square region with two adjoining semicircular regions whose diameters are two opposite sides of the square. The radius of each semicircle is 10 meters. The garden will be surrounded along its edge by a sidewalk with a uniform width of 1.5 meters. What will be the area of the sidewalk, in square meters?

A. 60
B. 80
C. 130
D. 140
E. 160
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The problem says the semicircular regions are adjoining the opposite side of squares. So they will be as shown in below image.
After solving the answer would come approximately 160 square meters.

Attachment:
pic (2).png
pic (2).png [ 543.5 KiB | Viewed 2031 times ]
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georgecambridge
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A garden located on level ground is in the shape of a square region 07 Jun 2023, 07:33
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can you provide detailed computations please? I cannot arrive at the answer.
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A garden located on level ground is in the shape of a square region 07 Jun 2023, 19:19
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Divide the area in two parts to calculate total area-

1. Calculate the area between two adjacent semicircles.
For easier calculations we can think of TWO semicircles as ONE circle.

Area =Area of bigger circle - Area of smaller circle
=\(pi (11.5 )^2 - pi (10)^2\)
= \(132.25 pi - 100 pi\)
=\( 32.25 pi\)
= \(101.265\)


2. Central area = Area of rectangle - Area of square
= 23*20 - 20*20
=60

Total Area = 161.265
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