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Brut [27]
3 years ago
13

3. Audrey measures the distance around the lid of her aquarium. The picture

Mathematics
1 answer:
alekssr [168]3 years ago
7 0

Answer:

Answer: 10 inches

Explanation: You are given one side of the aquarium which is 18 inches. The top and the bottom of the aquarium is 18 inches because that’s what the diagram gives us. So you can multiply 18 x 2=36. Now, to find the missing side length, subtract the perimeter (56 inches) by 36 and you get 20 inches. However, that’s not your final answer because you have to divide 20/2=10 inches. 10 inches is the missing side length for the left and right side lengths

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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
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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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