Question 1

In a regular polygon, each central angle measures 15°. How many sides does the polygon have?

Accepted Answer

The answer of In a regular polygon, each central angle...

Question 2

If    , then the areas of  and  are equal.

Accepted Answer

The given codes are hexadecimal codes that do not provide any information relevant to the areas of two shapes. Therefore, the statement is not related to the codes and does not provide enough information to determine whether the areas are equal or not. The answer is purely based on logic, and since there is no provided information to suggest that the areas are different, the statement can be assumed to be true.

Question 3

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

Accepted Answer

The answer of In  , m  = 90°....

Question 4

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 5

-In a regular pentagon, each side has the length 4.8 inches while the apothem has the length 7.4 inches. To the nearest tenth of an inch, find the length of the radius of the pentagon.

Accepted Answer

The answer of 
-In a regular pentagon, each side has...

Question 6

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 7

-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  ,    and...

Question 8

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

Accepted Answer

The area of a circle is given by A = πr^2. The given formula is incorrect.

Question 9

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

Accepted Answer

The answer of 
-In  ,    and...

Question 10

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

The area of a triangle with an inscribed circle of radius r is given by A = r * s, where s is the semi-perimeter of the triangle, not the full perimeter P.

Question 11

In a regular polygon with center O and a side  , m  = 72°. If AB = 4.6 inches, find the perimeter of the regular polygon.

Accepted Answer

The answer of In a regular polygon with center O...

Question 12

In regular octagon ABCDEFGH, AB = 6. Find the perimeter of trapezoid ABCH.

Accepted Answer

The answer of In regular octagon ABCDEFGH, AB = 6....

Question 13

In regular hexagon ABCDEF, AB = 12. Find the length of diagonal  .

Accepted Answer

The answer of In regular hexagon ABCDEF, AB = 12....

Question 14

-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

A square foot is a unit of area that is a square with sides of 1 foot each. Since 1 foot equals 12 inches, the area in square inches is 12 inches * 12 inches = 144 square inches.

Question 15

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 16

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 17

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 18

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

Accepted Answer

The answer of The area of the trapezoid with base...

Question 19

For two similar triangle, the ratio of two corresponding sides is  :  = 1:3.
Find the ratio of their areas  :  .

Accepted Answer

The answer of For two similar triangle, the ratio of...

Question 20

-In an equilateral triangle whose radius has length 6, find the length of an apothem.

Accepted Answer

The answer of 
-In an equilateral triangle whose radius has...

Quiz 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

In a regular polygon, each central angle measures 15°. How many sides does the polygon have?

If , then the areas of and are equal.

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

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

-In a regular pentagon, each side has the length 4.8 inches while the apothem has the length 7.4 inches. To the nearest tenth of an inch, find the length of the radius of the pentagon.

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

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

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

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

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

In a regular polygon with center O and a side , m = 72°. If AB = 4.6 inches, find the perimeter of the regular polygon.

In regular octagon ABCDEFGH, AB = 6. Find the perimeter of trapezoid ABCH.

In regular hexagon ABCDEF, AB = 12. Find the length of diagonal .

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

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

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?

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

For two similar triangle, the ratio of two corresponding sides is : = 1:3. Find the ratio of their areas : .

-In an equilateral triangle whose radius has length 6, find the length of an apothem.