Area of Composite Figures Assignment

What is the area of the composite figure? _____ units2

34

A new business requires an office space of at least 110,000 square meters. Is there enough space in the floor plan shown here? The radius of the semicircle is ________ The area of the office shown in the floor plan _______

100m is greater than what the business needs

The window shown is the shape of a semicircle with a radius of 6 feet. The distance from F to E is 3 feet and the measure of = 45°. Find the area of the glass in region BCIH, rounded to the nearest square foot. ___ ft2

11

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?

a. (60 - 15π) square inches

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.

a. 4A + B d. 1.5B e. 12A

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.

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

a. as two semicircles and a rectangle

An equilateral triangle with side lengths equal to units is inscribed in a circle. 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. Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (π − ) units2.

6 12 48 36

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. Shaded area = area of the ______ - area of the ________ + area of the _________ - area of the __________

regular hexagon regular pentagon square equilateral triangle