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Area of Semi Circle: Definition and Examples | EDU.COM

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Area of Semi Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Area of Semi CircleArea of Semi Circle: Definition and ExamplesTable of ContentsArea of a Semicircle Definition of Area of Semicircle

A semicircle is half of a circle, formed when we divide a circle into two identical halves by drawing a line (diameter) through the center of the circle. Every diameter of a circle divides it into two semicircles. When folded along its diameter, a circular piece forms a semicircle.

The area of a semicircle is half the area of a circle with the same radius. Since the area of a circle is πr2\pi r^2πr2, the area of a semicircle can be calculated using the formula πr22\frac{\pi r^2}{2}2πr2​ or 12πr2\frac{1}{2}\pi r^221​πr2. Alternatively, if we know the diameter (ddd) of the semicircle, we can use the formula πd28\frac{\pi d^2}{8}8πd2​ to find its area, where r=d2r = \frac{d}{2}r=2d​.

Examples of Area of Semicircle Example 1: Finding the Area of a Semicircle Given the Radius Problem:

If the radius of a semicircle is 494949 inches, find its area.

Step-by-step solution:

Step 1, Identify what we know. The radius (rrr) = 4949 49 inches.

Step 2, Recall the area formula for a semicircle: Area of semicircle=πr22\text{Area of semicircle} = \frac{\pi r^2}{2}Area of semicircle=2πr2​

Step 3, Substitute the value of radius and π. Let's use π=227\pi = \frac{22}{7}π=722​ for our calculation.

Area of semicircle=227×4922\text{Area of semicircle} = \frac{22}{7} \times \frac{49^2}{2}Area of semicircle=722​×2492​

Step 4, Simplify the calculation.

Area of semicircle=11×7×49\text{Area of semicircle} = 11 \times 7 \times 49Area of semicircle=11×7×49

Area of semicircle=3,773 inches2\text{Area of semicircle} = 3,773\text{ inches}^2Area of semicircle=3,773 inches2

Example 2: Finding the Area of a Semicircle Given the Diameter Problem:

If the diameter of a semicircle is 707070 inches, find its area.

Step-by-step solution:

Step 1, Convert the diameter to radius. Since the radius is half of the diameter:

Radius=702=35 inches\text{Radius} = \frac{70}{2} = 35 \text{ inches}Radius=270​=35 inches

Step 2, Use the area formula for a semicircle: Area of semicircle=πr22\text{Area of semicircle} = \frac{\pi r^2}{2}Area of semicircle=2πr2​

Step 3, Substitute the value of radius and π. Using π=227\pi = \frac{22}{7}π=722​:

Area of semicircle=227×3522\text{Area of semicircle} = \frac{22}{7} \times \frac{35^2}{2}Area of semicircle=722​×2352​

Step 4, Simplify the calculation.

Area of semicircle=11×5×35\text{Area of semicircle} = 11 \times 5 \times 35Area of semicircle=11×5×35

Area of semicircle=1,925 inches2\text{Area of semicircle} = 1,925 \text{ inches}^2Area of semicircle=1,925 inches2

Example 3: Finding the Combined Area of a Square and Semicircle Problem:

Find the area of the figure in which ABCD is a square of side 424242 inches and CPD is a semicircle. (Use π=227\pi = \frac{22}{7}π=722​)

Area of Semicircle

Step-by-step solution: Step 1, Break down the problem. We need to find: The area of the square ABCD The area of the semicircle CPD Add these two areas together

Step 2, Calculate the area of the square.

Area of square=side2=422=1,764 square inches\text{Area of square} = \text{side}^2 = 42^2 = 1,764 \text{ square inches}Area of square=side2=422=1,764 square inches

Step 3, Find the radius of the semicircle.

Since the semicircle CPD is built on the side CD of the square, the diameter equals the side length (424242 inches). So:

Radius=422=21 inches\text{Radius} = \frac{42}{2} = 21 \text{ inches}Radius=242​=21 inches

Step 4, Calculate the area of the semicircle.

Area of semicircle=12×π×r2=12×227×212=693 square inches\text{Area of semicircle} = \frac{1}{2} \times \pi \times r^2 = \frac{1}{2} \times \frac{22}{7} \times 21^2 = 693 \text{ square inches}Area of semicircle=21​×π×r2=21​×722​×212=693 square inches

Step 5, Find the total area by adding the areas.

Total area=1,764+693=2,457 square inches\text{Total area} = 1,764 + 693 = 2,457 \text{ square inches}Total area=1,764+693=2,457 square inches

Comments(4)AAppDeveloperYuriNovember 6, 2025I've been struggling to explain semi - circle area to my students. This page's defs and examples made it super easy! Thanks!

RReaderAliceNovember 6, 2025I've used this area of semi circle def for my kid's study. The examples made it easy to grasp, especially with combined shapes. Great resource!

DDesignerNinaNovember 4, 2025I've used this glossary page to teach semi-circle area. The examples are great! Really helped my students grasp the concept.

MCMs. CarterSeptember 17, 2025This definition and examples on the area of a semicircle were so clear! I used it to help my son with his homework, and he finally understood how the radius and diameter work together. Thanks, EDU.COM!

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