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1. Angles and Lines
2. Intersecting Angles
3. Triangles
4. Circles
5. Perimeters & Areas
6. Solids
7. Coordinate Geometry

Perimeters and Areas

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

Circle P= 2r A=r	Rectangle P= 2h + 2b
Square P = 4h A = h	Right triangle A = bh / 2
Triangle A = bh/2	Parallelogram A = bh

Example 1

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

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

Example 2

An automobile travels 2 miles. How many rotations does a 14-inch radius tire make?

Solution
The circumference of a tire is 2r = 2 x 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 x 5280 x 12)/28

No. of rotations = (5280 x 12 x 7)/(14 x 22) = (5280 x 3)/11= 1440

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.

Example 3

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.

Solution
First, sketch the figure. The area of the circle is r = 100. That's easy.

 

Now let's go over the area of the circle. The diameter is 20, which is also equal to the diagonal of the square. The diagonal of the square is also the hypotenuse of a right triangle inside of the square, a 45-45 triangle.

The legs of the triangle are equal so that b = 20/. Since it is a 45/45 right triangle, the legs are equal to the hypotonuse /. The area of the square is the legs squared (20 / ) = 200. The ratio of the areas is

Area circle/Area square = 100/200 =/2

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