A circle is a round shape, with no corners, where all radii (distance from the edge to the center) is the same. A semicircle takes the circle and cuts it in half through the diameter (a line that goes from one edge of the circle to the other side and passes through the center of the circle), in other words it is half of a circle. A semicircle can be closed off with a line, creating a semicircle shape, or it can be left with no line, creating a semicircle arc. Typically when referring to a semicircle the, shape with the line closing the bottom is being referenced.
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The area of a semicircle refers to the amount of area inside of the lines of the semicircle shape. The semicircle arc has no area since it is not closed off into a shape. Area is given in units that are 'squared', such as square inches or square meters. The term 'squared' comes from how formulas for area is derived, based on how many individual square shapes can fit inside the lines of the shape.
To find the area of a circle, the formula is pi times the radius squared. Since a semicircle is half of a circle, the area of a semicircle is half of a circle. So the formula to find the area of a semicircle is pi times radius squared divided by 2, or pi times diameter squared divided by 8:
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In this formula r refers to the radius of the semicircle (or the radius of the corresponding circle), and d refers to the diameter. Either formula can be used depending on what information is provided.
Let's first find the area of a semicircle when given the radius:
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In this semicircle, the radius is equal to 3 cm. Put '3' in for r in the formula to find the area of a semicircle with a radius of 3 cm.
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So the area of this semicircle is 14.1 cm2
Now let's find the area of a semicircle from the diameter:
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The diameter is equal to 12 cm, so put in '12' for d in the formula:
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This semicircle has an area of 56.5 cm2.
The perimeter refers to the length of the line going around the entire shape. It is how long the line would be if the line was laid out in one straight line. It is the distance to walk around the entire shape. The perimeter of a semicircle is equal to the length of the arc and the length of the line connecting the two ends of the arc. The perimeter of a semicircle arc is simply the length of the arc.
The formula to find the perimeter of a circle (also called the circumference) is pi times the diameter (or pi times two time the radius). But the formula to find the perimeter of a semicircle isn't just half of the perimeter of the circle (that would be the perimeter of a semicircle arc), the additional length of the diameter needs to be added. This means that the perimeter of semicircle formula is:
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In these equations d refers to the diameter and r refers to the radius.
Given the radius of a semicircle is 30 meters, determine the perimeter of the semicircle. The number 30 can replace r in the simplified formula, where pi plus 2 is all multiplied by the radius:
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This gives a perimeter of 154.2 meters (the units for perimeter are not squared like for area).
Now, given the diameter of 24 meters, determine the perimeter of the semicircle. First, divide 24 by 2 to get 12 for the radius; then 12 can replace r in the formula:
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This gives a perimeter of 61.7 meters.
An inscribed angle in a semicircle is when a line is drawn from each end of the diameter to a point on the arc, forming a triangle. The inscribed angle in the angle formed at the point of the triangle.
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Since a semicircle has a constant arc (at 180 degrees) and all distances from the center are the same, the inscribed angle will always be the same, and exactly half of the angle of the arc, which is 90 degrees, or a right angle.
A semicircle is half of a circle, or a round shape where all distances from the center are the same. The semicircle is cut through the diameter of the circle. The area of a semicircle is half the area of the circle. The perimeter of a semicircle is half the perimeter of the circle plus the diameter. The formulas for the area and perimeter of a semicircle are:
The radius is half of the diameter, and the diameter is the length of the semicircle. The units used for area and perimeter are:
The angled inscribed in a semicircle, which is the angle formed when a triangle is formed from each end of the diameter of the semicircle, is always 90 degrees.
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A semicircle is a partial circle. The moon looks like a partial circle to us unless it's full or not visible. Let's do a word problem that deals with calculating the perimeters and areas of partial circles.
You have decided to make a partial circle flower bed in your yard. You want the diameter of the partial circle to be 20 feet. You want to put a stone border around the entire partial circle and mulch inside the partial circle that's 2 inches deep.
1. If each stone costs $1.25 and is 5 inches long, how much are you going to spend on buying stones for the border?
2. Each bag of mulch contains 3 ft3. How many bags of mulch do you need to buy?
1. First we need to determine the perimeter of the flower bed. This involves the curved section (C) and the diameter (d):
Adding this result to the diameter, we get 31.4 ft + 20 ft = 51.4-feet perimeter.
Dividing the perimeter by the length of a stone gives us the quantity of stones needed. However, we need to convert the perimeter into inches:
Now we can calculate the cost of the stones:
124 x $1.25 = $155
2. The volume of mulch needed is the area of the semicircle multiplied by the depth of the mulch:
The depth of the mulch is in inches, so we'll multiply the area by (2/12), which is the depth in feet:
Dividing the volume by the volume of the mulch in the bag will give us the number of bags of mulch needed:
6.54 / 3 = 2.18 bags, which we will round to three bags.
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