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Yanka [14]
2 years ago
11

I need help with this problem. Given: BC = 10 inches AC = √50 inches m∠CBD = 60° m∠CAD = 90° Calculate the exact area of the sha

ded region. Show all work for full credit. picture shown!

Mathematics
1 answer:
Nikitich [7]2 years ago
8 0

Answer:

Area of the shaded region = 23.33 in²

Step-by-step explanation:

Area of a sector = \frac{\theta}{360}(\pi r^{2})

Where θ = Central angle subtended by an arc

r = radius of the circle

Area of the sector BCD = \frac{60}{360}(\pi) (10^{2})

                                       = 52.36 in²

Area of equilateral triangle BCD = \frac{\sqrt{3} }{4}(\text{Side})^2

                                                      = \frac{\sqrt{3} }{4}(10)^2

                                                      = 25\sqrt{3} in²

                                                      = 43.30 in²

Area of the shaded portion in ΔBCD = 52.36 - 43.3

                                                             = 9.06 in²

Area of sector CAD = \frac{90}{360}(\pi)(\sqrt{50})^2

                                 = 39.27 in²

Area of right triangle CAD = \frac{1}{2}(\text{Base})(\text{Height})

                                            = \frac{1}{2}(\text{AC})(\text{AD})

                                            = \frac{1}{2}(\sqrt{50})(\sqrt{50})

                                            = 25 in²

Area of the shaded part in the ΔACD = 39.27 - 25

                                                                         = 14.27 in²

Area of the shaded part of the figure = 9.06 + 14.27

                                                                = 23.33 in²

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The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area
miv72 [106K]

Answer:

20 square feet

Step-by-step explanation:

The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area

Step 1

We find the Length and Width of the deck

Perimeter of a rectangle = 2L + 2W

The length of a rectangular deck is five times it's width

W = Width

L = Length = 5W

P = 24 feet

Perimeter = 2(5W) + 2W

24 = 10W + 2W

24 = 12 W

W = 24/12

W = 2 feet

Solving for L

L = 5W

L = 5 × 2 feet

L = 10 feet

Step 2

We find the area of the deck

Area of the deck(Rectangle) = Length × Width

= 10 feet × 2 feet

= 20 square feet

4 0
2 years ago
How to solve it and understand it
algol13

Volume of rectangle prism = w l h

Volume of rectangle pyramid = 1/3(w l h)

so Volume of rectangle pyramid = 1/3 (Volume of rectangle prism)

= 1/3 (240)

= 80

Answer:

80 cm^3

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Previous
o-na [289]
Total weight of the 8 backpacks = 8 x 14 = 112 pounds

Total weight of the 12 backpacks = 12 x 9 = 108 pounds

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Mean weight of the 20 backpacks = 220 ÷ 20 = 11 pounds

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Answer: The mean weight of the 20 backpacks is 11 pounds
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