Question 1

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

Accepted Answer

NOT ANSWERED.

Question 2

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

Accepted Answer

NOT ANSWERED.

Question 3

If        , then the areas of  and  are equal.

Accepted Answer

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.

Accepted Answer

This is known as the inradius formula, and it is true for all triangles.

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  .

Accepted Answer

The answer of  and  have the same length...

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

Accepted Answer

To find the number of square inches in one square foot, we need to square the conversion factor, 1 foot = 12 inches:
(1 foot)^2 = (12 inches)^2 = 144 square inches. Therefore, one square foot has 144 square inches.

Question 7

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

Accepted Answer

Two triangles can have the same area and the same altitude length but differ in shape, making them not congruent. For example, a right-angled triangle and an isosceles triangle can share these characteristics without being 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.

Accepted Answer

The answer of For a square whose length of apothem...

Question 9

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

Accepted Answer

The answer of What expression represents the exact circumference of...

Question 10

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

Accepted Answer

The answer of In  ,      ...

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)

Accepted Answer

The answer of In kite HJKL , HJ = HL...

Question 12

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

Accepted Answer

The answer of Given that 1 foot = 12 inches,...

Question 13

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

Accepted Answer

The answer of If the area of quadrilateral ABCD is...

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

Accepted Answer

Let the sides of the triangle be $a$, $b$, and $c$. Then the perimeter $P$ is given by $P=a+b+c=36$. Also, the area $K$ of the triangle is given by $K=rs$, where $r$ is the inradius and $s$ is the semiperimeter ($s=P/2$). Therefore, we have $K=3s=3(P/2)=54$. Thus, the answer is $\boxed{	extbf{(B) }54}$.

Question 15

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

Accepted Answer

The answer of For the right triangle with sides of...

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.

Accepted Answer

The answer of In  ,      ...

Question 17

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

Accepted Answer

The answer of Assuming that       ...

Question 18

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

Accepted Answer

The answer of Write the formula for the area A...

Question 19

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

Accepted Answer

The formula for the area of a circle is A = πr^2, where π is approximately 3.14. The given formula is not correct as it doesn't include π.

Question 20

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

Accepted Answer

This is the formula for the area of a trapezoid, so it is true.

Quiz 9: Areas of Polygons and Circles

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

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

If , then the areas of and are equal.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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