Deck 9: Areas of Polygons and Circles

Question 1

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

Answer 1

NOT ANSWERED.

Question 2

In , m = 90 ° . What fraction represents the part of the circumference that is the length of ?

Answer 2

NOT ANSWERED.

Question 3

If     , then the areas of and are equal.

Answer 3

False

Question 4

Where P is the perimeter of a triangle whose inscribed circle has radius length r,the area of the triangle is A = rP.

Question 5

and have the same length of base and the same length of altitude.
If the area of is 25 , find the area of .

Question 6

Given that 1 foot = 12 inches, find the number of square inches in one square foot.

A)12
B)24
C)144
D)None of These

Question 7

If two triangles have the same areas and the same length of altitude, these triangles must be congruent.

Question 8

For a square whose length of apothem is a, find an expression containing a that represents the area A of the square.

Question 9

What expression represents the exact circumference of a circle with radius 6 inches?

Question 10

In ,     and     . If AB = 16, BC = 12, and BH = 14, find the length of altitude to side .

Question 11

In kite HJKL , HJ = HL and JK = LK . If m = 90 ° , HJ = 12, and JK = 5, find the length of diagonal .

A)
B)
C)
D)

Question 12

Given that 1 foot = 12 inches, what is the number of square inches in 1 square foot?

Question 13

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

Question 14

For a triangle whose perimeter measures 36 units, the radius of the inscribed circle is 3.Find the area of the triangle.

A)27
B)54
C)108
D)None of These

Question 15

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

Question 16

In ,     and in ,     . If AB = XY and CD = ZW , then:

A)
B)
C) and have the same perimeter.
D) and have the same area.

Question 17

Assuming that     and     in , what line segment is the altitude of this parallelogram with respect to side ?

Question 18

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

Question 19

For a circle of radius r , the area is given by A = 2 r .

Question 20

The area of the trapezoid with base lengths and and altitude h is given by A = h (  + ).

Question 21

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

Question 22

Find the exact area of a triangle whose sides measure 5, 6, and 7.

A)
B)
C)
D)None of These

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Question 27

In ,     . If MQ = 10, RP = 4, and MR = 8, find the area of .

Question 28

The diagonals of quadrilateral ABCD are perpendicular. If AC = 14 inches and BD = 25 inches, find the area of ABCD.

Question 29

The semiperimeter s of a triangle with sides of lengths a , b , and c is given by s = ( a + b + c ).

Question 30

In isosceles trapezoid HJKL ,     . If m = 45 ° , JK = 6 cm, and the length of an altitude is 4 cm, find the exact perimeter of HJKL .

A)(20 + 4 )cm
B)(20 + 8 )cm
C)(20 + 4 )cm
D)(20 + 8 )cm

Question 31

A triangle has a perimeter of 40 and area of 60. Using A = rP , find the length
of radius r for the inscribed circle for this triangle.

Question 32

Find the area of the triangle whose sides have lengths 13 cm, 14 cm, and 15 cm.

Question 33

If both a parallelogram and triangle have the same base and altitude, then thearea of the parallelogram is twice the area of the triangle.

Question 34

In ,     and     . How are and related?

A)congruent
B)same perimeters
C)same areas
D)similar

Question 35

Find the length of base in an isosceles triangle with perimeter 25 inches and length of leg8 inches.

Question 36

For the triangle with sides of lengths a, b, and c, find an expression for the semiperimeter s of the triangle.

Question 37

If , then the altitude to base of is .

Question 38

The area of is 35.1 . Choosing a side of RSTV that measures 4.5 cm as the base, what is the length of the corresponding altitude?

A)7.8 cm
B)8.2 cm
C)15.6 cm
D)None of These

Question 39

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

Question 40

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

Question 41

A square is inscribed in a circle. If the area of the circle is 28.25 and the area of the square is 18 , find the area of the four-part region that lies outside the square but inside the circle.

Question 42

The region bounded by chord and arc is known as a segment of the circle.

Question 43

If a sector of a circle has arc measure 120°, then its area equals one-third the area of the circle.

Question 44

If the area of a regular octagon is 25 , find the area of the regular octagon whose sides are twice those of the first octagon.

A)50
B)25
C)50
D)None of These

Question 45

For a regular octagon, the length of the apothem is a = 8.2 cm while the length of each side is s = 6.7 cm. To the nearest tenth of a square centimeter, find the area of the regular octagon.

Question 46

For a regular pentagon, find the measure of each central angle.

Question 47

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

Question 48

For a square with apothem of length a, the perimeter equals 4a.

Question 49

The pentagon shown is composed of square ABCD and isosceles triangle BXC in which m = 90 ° . If AD = 4 cm, find the area of the pentagon.

Question 50

The area of any regular polygon with length of apothem a and perimeter P is given by A = aP .

Question 51

To the nearest tenth of a foot, find the circumference of a circle whose length of diameter is 12.6 feet.

Question 52

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

Question 53

A square has an area of 13 . What is the exact length of each side of the square?

Question 54

The area of an equilateral triangle with sides of length s is given by A = .

Question 55

For a given circle, the length of a 90° arc is one-third the circumference of the circle.

Question 56

If m = 45 ° and OA = 4.3 cm, find l correct to the nearest tenth of a centimeter.

Question 57

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.

A)64.2
B)65.1
C)97.6
D)130.2

Question 58

Find the area of a square whose apothem has length 7 cm.

A)14
B)28
C)98
D)196

Question 59

The radius of an equilateral triangle measures 4 inches. Find the area of this equilateral triangle.

Question 60

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

A)9
B)9
C)54
D)54

Question 61

For the segment shown, let the center of the circle be point O. If the area of the related sector bounded by and and arc is 45 while the area of is 28 , find the area of the segment bounded by and .

Question 62

In , a sector is bounded by radii and and arc . If m = 90 ° and PX = 6 m, find the exact area of the sector.

A)9
B)12
C)3
D)36

Question 63

For the segment bounded by chord and arc , CD = 12 cm and m = 120 ° .Find the exact area of the segment.

A)48
B)(48 18 )
C)(48 36 )
D)None of These

Question 64

In , m = 45 ° and OA = 6 cm. Find .

A)1.5 cm
B)3 cm
C)6 cm
D)12 cm

Question 65

Where C is the circumference of a circle and r is its length of radius, the approximate value of the ratio C : r is:

A)1.57
B)3.14
C)6.28
D)12.56

Question 66

For the right triangle with sides of lengths 5 in, 12 in, and 13 in, find the length of the radius of the inscribed circle.

A)2 inches
B)2.5 inches
C)3 inches
D)3.5 inches

Question 67

Using   3.14, find the approximate area of a circle with radius r = 10 cm.

Question 68

Where R is the radius of the larger circle and r is the radius of the smaller circle, the area of the ring (or annulus)is given by A = .

Question 69

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.

Question 70

In a circle of radius length 5, use an inequality of the form a x b to express possible lengths x for a chord.

Question 71

The area of a circle is 27.5 . To the nearest tenth of a square inch, find the area of the square that is circumscribed about this circle.

Question 72

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

A)6.3 cm
B)12.7 cm
C)19.0 cm
D)None of These

Question 73

For , radii and and arc bound a sector. If m = 100 ° and PX = 5.6 inches, find the area of the sector correct to the nearest tenth of a square inch.

Question 74

Using     , find the approximate area of a circle with a diameter of length 7 inches.

A)19.25
B)38.5
C)77
D)154

Question 75

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 .

Question 76

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

Question 77

If m = 50 ° , then what fraction of the area of the circle represents the area of the sector shown?