Area of Composite Figures

Question 1

The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B cm2. Which expressions show the area of the shaded region in terms of A and B? Check all that apply.

Revolt · Accepted Answer

4A + B; 1.5B; 12A

Question 2

For a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. How much paper is wasted?

Revolt · Accepted Answer

(60 – 15π) square inches

Question 3

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?

Revolt · Accepted Answer

Isla is correct because each figure subtracts an equal area from the area of the square.

Question 4

Question 4

Revolt · Accepted Answer

34

Question 5

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

Revolt · Accepted Answer

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

Question 6

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.

Revolt · Accepted Answer

✔ regular hexagon; 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

Question 7

square✔ regular pentagonregular hexagon

Revolt · Accepted Answer

✔ regular pentagon

Question 8

equilateral triangle✔ squareregular pentagon

Revolt · Accepted Answer

✔ square

Question 9

✔ equilateral trianglesquareregular hexagon

Revolt · Accepted Answer

✔ equilateral triangle

Question 10

A new business requires an office space of at least 110,000 square meters. Is there enough space in the floor plan shown here?

Revolt · Accepted Answer

✔ 100 m; The radius of the semicircle is .: 100 m; The area of the office shown in the floor plan .: is greater than what the business needs

Area of Composite Figures Answers

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