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miskamm [114]
3 years ago
12

Suppose a square ABCD has a side length of 1 unit. The arcs BD and AC are circular arcs with centers at A and D, respectively. F

ind the area of the shaded region.

Mathematics
1 answer:
Likurg_2 [28]3 years ago
6 0

Answer:

1-\frac{\sqrt{3} }{4}-\frac{\pi}{6}

Step-by-step explanation:

The missing figure is shown in the attachment

The area of the shaded region = Area of Square - (Area of sector AOB + Area of equilateral  triangle BOC + Area of sector COD)

Area of Sector AOB=Area of Sector COD=\frac{30}{360}*\pi*1^2=\frac{\pi}{12}

Area of equilateral triangle =\frac{1}{2}*r*\frac{\sqrt{3} }{2}*r=  \frac{1}{2}*1*\frac{\sqrt{3} }{2}*=\frac{\sqrt{3} }{4}

Area of shade region =1^2-\frac{\sqrt{3} }{4}-\frac{\pi}{12}*2

1-\frac{\sqrt{3} }{4}-\frac{\pi}{6}

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Can someone explain this step by step? I'm very confused on how to solve it. Thanks!
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Step-by-step explanation:

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3 0
2 years ago
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The surface area of a rectangular prism with length l, width w, and height h is given by the expression 2lw+2lh+2wh. Write an eq
Yuki888 [10]

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Step-by-step explanation:

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4 0
2 years ago
What is the next term in the geometric sequence 4, -12, 36
Ilia_Sergeevich [38]
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7 0
3 years ago
On one day, 4 chefs and 5 helpers earned $650.
Arlecino [84]
4c + 5h = 650 and

5c + 6h = 800 where c are chefs, h are helpers

Start by finding an expression for c

4c + 5h = 650
4c = 650 -5h
c = (650- 5h)/4

Then substitute that into the second equation and solve for a number value for h
5 (650-5h)/4 + 6h = 800
(3250-25h)/4 + 6h = 800
Multiply both sides by 4
3250-25h + 24h = 3200
-h = -50
h = 50

Take that 50 and substitute it into the expression we have for c to get a number value for c

C= 650-5(50)/4
C = 650-250/4
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Check your first equations, substituting $50 for the helpers and $100 for the chefs.

4 (100) + 5(50) =
400 + 250 = 650

5(100) + 6(50) =
500 + 300 = 800
6 0
3 years ago
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