Area of Composite Figures Answers

33 verified answers2 views
1
Free Preview

How can you decompose the composite figure to determine its area?

A
as two semicircles and a rectangle
B
as two circles and a rectangle
C
as a circle and a square
D
as two semicircles and a trapezoid
2
Free Preview

square✔ regular pentagonregular hexagon

A
square
B
✔ regular pentagon
C
regular hexagon
3

equilateral triangle✔ squareregular pentagon

A
equilateral triangle
B
✔ square
C
regular pentagon
4

✔ equilateral trianglesquareregular hexagon

A
✔ equilateral triangle
B
square
C
regular hexagon
118847

✔ is greater than what the business needsis less than what the business needsis exactly 110,00 square feetcannot be determined with the information given

A
✔ is greater than what the business needs
B
is less than what the business needs
C
is exactly 110,00 square feet
D
cannot be determined with the information given
118865

⇒ 11

Answer:

118865

118868

Isla says the areas of the two shaded regions are equal. Clara says the shaded region in the first figure has a larger area. Who is correct?

A
Isla is correct because each figure subtracts an equal area from the area of the square.
B
Isla is correct because it is the sum of the area of the circle and the area of the square.
C
Clara is correct because the area of the circle is less than that of the two semicircles.
D
Clara is correct because the area of the two semicircles is less than that of the circle.
118869

⇒ 34

Answer:

118840

118870

An equilateral triangle with side lengths equal to units is inscribed in a circle.

Answers:
Half a side length of the equilateral triangle is units, so the apothem is units long and the radius of the circle is units long.:6
Half a side length of the equilateral triangle is units, so the apothem is units long and the radius of the circle is units long.:12
Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (π − ) units2.:48
Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (π − ) units2.:36
118871

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the area of the shaded regions.

Answers:
Shaded area = area of the – area of the + area of the – area of the:regular hexagon
Shaded area = area of the – area of the + area of the – area of the:regular pentagon
Shaded area = area of the – area of the + area of the – area of the:square
Shaded area = area of the – area of the + area of the – area of the:equilateral triangle
118872

An equilateral triangle with side lengths equal to units is inscribed in a circle.

Question illustration
Answers:
Half a side length of the equilateral triangle is units, so the apothem is units long and the radius of the circle is units long.:6
Half a side length of the equilateral triangle is units, so the apothem is units long and the radius of the circle is units long.:12
Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (π − ) units2.:48
Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (π − ) units2.:36
118873

69✔ 12

A
6
B
9
C
✔ 12
118874

4✔ 48144

A
4
B
✔ 48
C
144
118875

612✔ 36

A
6
B
12
C
✔ 36
118876

How can you decompose the composite figure to determine its area?

A
as two semicircles and a rectangle
B
as two circles and a rectangle
C
as a circle and a square
D
as two semicircles and a trapezoid

Did you find these answers helpful?