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2 years ago

A triangle is placed in a semicircle with a radius of 6 yd, as shown below. Find the area of the shaded region.

Mathematics

1 answer:

yulyashka [42]2 years ago

4 0

Answer: The area of the shaded region is 20.52 yd^2

Step-by-step explanation: The given figure shows a triangle inserted into a semi circle. The base of the triangle runs from one end of the semi circle to the other, which means the base of the triangle measures the same as the diameter. If the radius of the circle is 6, then the diameter equals 12 yds, (that is radius times 2).

The area of the triangle is given as;

1/2 b x h (that is)

1/2 base x height

Where the base is 12 and the height is 6. The area equals

Area = 1/2 (12) x 6

Area = 6 x 6

Area = 36 yd^2

Also to compute the area of the semi circle, we shall calculate the area of a circle and divide by 2.

Area of a circle is;

Area = pi x R^2

Area = 3.14 x 6^2

Area = 3.14 x 36

Area = 113.04

Area of semi circle = 113.04/2

Area of semi circle = 56.52 yd^2

At this point, subtracting the area of the triangle from the area of the semi circle leaves us with the area of the shaded region. Hence

Area of shaded region = 56.52 - 36

Area of shaded region = 20.52 yd^2

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3 years ago

Help and explain thanks!

katen-ka-za [31]

Answer:

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Step-by-step explanation:

One way to tackle this is by getting another sheet of paper and drawing it out, then counting up the total of the sides. If you draw it, you can see that you're dealing with a rectangle; two sides of length 12 and two sides of length 8. If you don't like drawing or don't want to in this case, another way to get the answer is by knowing one vertex is at (0, 0), so the next vertex (0, 8), would create a side that's exactly 8 units long. Kind of the same, you know from (0, 0), you also have a point (12, 0), so drawing that would create a side that's 12 units long. All in all, to get the perimeter in units, you have 12 + 12 + 8 + 8 = 40.

The problem says it wants the amount of wood in centimeters needed for the perimeter. What we just found was the perimeter in generic units, so if the problem says every "grid square", or unit, is 3 centimeters long, then all you have to do is take our result 40 and multiply it by 3 to get the number of centimeters. Your perimeter in centimeters would be 120 cm.

7 0

2 years ago

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Look at the grid, you can see that it has 100 units in all.

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2 years ago