How to Solve for a Perimeter & an Area

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Students learn how to determine the perimeter and area of two-dimensional shapes as part of their basic education in mathematics, and these formulas are among core concepts employed in higher levels of math. Finding the perimeter and area of shapes also serves practical functions in everyday life. Home owners, architects and others may need to find the perimeter and area of a building or room. Each measurement requires a simple but specific formula.

Perimeter

  • Study the basic shape. Look at the length of the sides. According to Scholastic, the perimeter of a shape is the total distance around the outside of a polygon. You can find the perimeter of any shape that has closed line segments, such as squares, rectangles and triangles.

  • Add together the length of the sides. If you are solving the perimeter for a rectangle, add together the width and the length so it looks like "w+w+l+l." A quick version of this calculation is to multiply two times the sum of the width and length, or "2(w+l)."

  • Solve the perimeter of a triangle. Add together all the sides in a calculation that looks like "side a + side b + side c."

  • Find the perimeter of a square. Add together all of the sides, which are equal in length, or multiply one of the sides by four to get your answer for the perimeter. For instance, if the sides of your square are all 4 feet, you could multiply 4 times 4 to get a perimeter of 16. You could also add 4+4+4+4 to get 16.

Area

  • Know the length and width of the shape for which you want to find the area. Finding the area calls for the use of multiplication.

  • Solve the area of a rectangle. The calculation for finding the area of a rectangle is "length x width = area." If the length of the rectangle is 4 and the width is 2, multiply 4 times 2 to get an area of 8.

  • Find out the area of a triangle. This calculation is a little different because you need to know the base and height of the triangle. The calculation for a triangle follows the formula "area = 1/2(base x height)." If the base of your triangle is 4 feet and the height of your triangle is 3 feet, then you multiply 4 times 3 to get 12, and multiply 12 by one half to equal 6. The area of your triangle is 6.

  • Perform the calculation for the area of a square. Multiply the length of the side by 2, since all of the sides of a square are equal.

References

  • Photo Credit Jupiterimages/Goodshoot/Getty Images
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