Unit 3: Geometry
SMART Packet #3
Composite Figures
Student:
A.G.1
Teacher:
Standard
Find the area and/or perimeter of figures composed of polygons and circles or
sectors of a circle (Note: Figures may include triangles, rectangles, squares,
parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and
regular polygons (perimeter only)
Composite Figures
A composite figure is made up of two of more shapes.
Example 1: Find the area of the composite figure.
Step 1: Divide the figure into smaller shapes.
Step 2: Find the length, l, and width, w, of each rectangle.
l=6
l=6
w=2
w=2
Step 3: Find the area of each rectangle.
A = lw
A = lw
A =6(2)
A = 6(2)
A = 12
Step 4: Add the areas.
12 + 12 = 24
A = 12 .
The area of the composite figure is 28 square meters (m2).
PRACTICE, PART I
Find the area of each figure.
1.
2.
3.
4.
5.
Example 2
Find the distance around the composite figure. Give your answer in terms of π.
Step 1: Divide the figure into smaller shapes.
Step 2: Find the distance around each figure.
C = πd
C = π(10)
C = 10π
C=
*Multiply by
1
(10π)
2
1
because it is a semicircle
2
C = 5π
Step 3: Combine the distances found in step 2.
5π + 26
8 + 8 + 10 = 26
The distance around the composite figure is 5π + 26 meters.
PRACTICE, PART II
Find the distance around each composite figure.
6.
7.
8.
PRACTICE, PART III: REGENTS PREP
9. A window is made up of a single piece of glass in the shape of a semicircle and a
rectangle, as shown in the diagram below. Tess is decorating for a party and wants to
put a string of lights all the way around the outside edge of the window.
To the nearest foot, what is the length of the string of lights that Tess will need to
decorate the window?
10. A playground in a local community consists of a rectangle and two semicircles, as
shown in the diagram below.
Which expression represents the amount of fencing, in yards, that would be needed to
completely enclose the playground?
(1) 15π + 50
(3) 30π + 50
(2) 15π + 80
(4) 30π + 80
11. Luis is going to paint a basketball court on his driveway, as shown in the diagram
below. This basketball court consists of a rectangle and a semicircle.
Which expression represents the area of this basketball court, in square feet?
(1) 80
(3) 80 + 16π
(2) 80 + 8π
(4) 80 + 64π
12. Find the area of the shaded region in the figure shown below.
13. A designer created the logo shown below. The logo consists of a square and four
quarter-circles of equal size.
Express the exact area of the shaded region, in square inches, in terms of π .