Exam 9: Areas of Polygons and Circles

For any quadrilateral with perpendicular diagonals of lengths and , the area is given by A = .

Find the area of a regular hexagon whose sides measure 6 inches each.

In trapezoid RSTV ,     . If SR = TV = 6 cm, ST = 4 cm, and m = 60 ° , find the area of RSTV .

To the nearest tenth of square inch, find the area of the regular pentagon whose apothemmeasures 4.2 inches and whose sides measure 6.2 inches.

Find the perimeter of rhombus RSTV in which the lengths of diagonals are RT = 24 in and SV = 10 in.

For the right triangle with sides of lengths 8, 15, and 17, find the length of the radius of the inscribed circle.

For an isosceles triangle with length of leg s and length of base b, the perimeter Pis given by P = 2s + b.

The region bounded by radii and and arc is known as a secant of the circle.

For a rectangle with base length of 1 foot and height 6 inches, the area is 6 .

A circle has the area 126 . To the nearest tenth of a centimeter, find the length of its diameter.

In , chord is 12 inches long and m = 90 ° . Find the exact area of the segment bounded by and .

For regular pentagon ABCDE , diagonals and are drawn to form . Find m .

    . If AB = 4, XY = 10, and the area of is 7.8 , find the area of

For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number .

If the area of quadrilateral ABCD is 27 and the area of is 11 , find the area of pentagon ABXCD .

Write the formula for the area A of any quadrilateral that has perpendicular diagonals of lengths and .

For rectangle ABCD, AB = 5 inches while the length of a diagonal is AC = 13 inches. Find the area of the rectangle.

If     , then the areas of and are equal.

For , the radius has length r and m = 180 ° . In terms of r , write an expression for the perimeter of the sector bounded by diameter and .

For the concentric circles, the outer circle radius is R = 6 in while that of the inner circle is r = 3 in. Find the exact area of the annulus (ring)that is determined by the two circles.