# How to Calculate the Area of an Arch

Save

An arch consists of a rectangle with a sector of a circle on top of it. To calculate the area of an arch you must first calculate the area of the sector, then add the area of the rectangle to it. A sector of a circle is an interior portion of a circle bounded by two radii and an arc. An arc of a circle is any connected section of the circle's circumference. Arcs can be measured by the central angle, created by drawing radii from the endpoints of the arc, or by the length of the arc itself. The area of a sector can be calculated using the measure of the central angle, in radians.

### Things You'll Need

• Protractor
• Ruler
• Draw a line from one endpoint of the arch's curve to the other endpoint of the arches curve. This line will divide the arch into a half circle and a rectangle.

• Measure the length of the line and record this length for use later.

• Divide the length of the line by 2 to find the radius of the circle. Record this value for later use.

• Plug the radius of the circle into the equation A = (1/2)?r^2 for the variable r. Because we are measuring the area of a half circle; ?, the central angle, is equal to ? radians.

• Calculate the value of A and record the results for later use. This is the area of the sector at the top of the arch.

• Measure the distance from the bottom of the arch to the line drawn in Step 1.

• Multiply the distance measured in Step 6 by the length of the line measured in Step 2 to determine the area of the rectangle.

• ### Other People Are Reading

• Add the area of the rectangle, from step 7, to the area of the half circle, from step 5, to determine the total area of the arch.

## References

• Photo Credit Arch image by Semfamily from Fotolia.com
Promoted By Zergnet

## Resources

### You May Also Like

• Causes of Foot Arch Pain

Foot arch pain can be debilitating and frustrating. Understanding the causes of your foot arch pain may be what you need to...

• How to Calculate the Length of an Arc

There are many ways to find the length of an arc, and the calculation needed depends on what information is given at...

• How to Calculate Arc Area

An arc is a curved area of a circle that makes up part of its circumference. If you know the arc of...

• How to Find the Radius of an Arch

An arch, or arc, can be thought of as a small portion of the perimeter of a circle. Because the size of...

• How to Calculate an Archway

A curved archway adds an interesting architectural element to a home or office. Rather than a plain rectangular entrance way, building an...

• How to Calculate the Length of an Arch

Measuring the length of a arch is a fundamental concept that every student must understand as they delve into the increasingly advanced...

• How to Calculate Arch

If you are remodeling your home, it is probably because you trying to improve upon what you already have. Therefore, it is...

## Related Searches

Check It Out

### Can You Take Advantage Of Student Loan Forgiveness?

M
Is DIY in your DNA? Become part of our maker community.