Geometry Chapter 5: Perimeters and Areas

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The perimeter of a figure is the distance around the figure. The perimeter, P, and area, A, of common figures are shown.

Calculating Diagonals  
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Symmetry

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What is the radius of a circle if its circumference is numerically equal to twice its area?

 

Solution The perimeter is the same as the circumference = 2r. The area is r, so that 2r = 2(r ); therefore, r must equal 1.

Example 2 (medium)

An automobile travels 2 miles. How many rotations does a 14-inch radius tire make (use 22/7 for )?

Solution The circumference of a tire is 2r = 2 × 14 = 28 inches. First, make the units commensurate by converting miles to inches (12 inches in a foot, 5280 feet in a mile). No. of rotations = (2 miles × 5280 ft/mile × 12 inches/ft) 28 Substitute 22/7 for (we put 7 on top and 22 on bottom) (2 × 5280 × 12 × 7 ) 28 × 22 Cancel out 2 into 22, 7 into 28 to make 4 and then that 4 into 12. (2 × 5280 × 312 × 7 ) 28 × 22 11 (5280 × 3) = 1440 11 In the above, we simplified by canceling out common factors and then multiplied and divided. It is important to first simplify to save time in the final step.

A square is inscribed in a circle of radius 10. Determine the ratio of the area of the circle to the area of the square.

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Contents of Geometry Chapter: Table of Contents Chapter 1: Angles and Lines   Chapter 2: Intersecting Angles   Chapter 3: Triangles   Chapter 4: Circles   Chapter 5: Perimeters & Areas   Chapter 6: Solids   Chapter 7: Coordinate Geometry    Chapter 6: Solids

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