11-7 Area of Complex Figures
(pages 498-500)
Standard  P8
A complex figure is made of circles,
rectangles, squares, and other twodimensional figures.
To find the area of a complex figure, “cut”
the figure into familiar figures whose areas
you already know how to find.
Remember your formulas…
Example #1: Find the area of the complex figure.
The figure can be separated into a square and a triangle.
Area of square
A = s2
A = 102
A = 100 ft2
Area of triangle
A = ½bh
A = ½· 10 • 6
A = ½ • 60
A = 30 ft2
Add the areas of the simple figures, 100 + 30.
The area of the complex figure is 130 square feet or 130 ft2.
Example 2: Find the area of the complex figure
• The figure can be separated into a
semicircle and a triangle.
Area of semicircle
A 
A 
1
2
1
r
2
  2
2
2
A  6 . 3in
2
Example 2 (continued)
Area of triangle
A 
A
1
2
1
bh
 4  3 .5
2
A7
Add the areas together:
6.3 + 7 = 13.3
The area of the figure is about 13.3 in2.
Example #3
SHORT ANSWER (2 Points):
“Triangle a” A= ½•bh
The plans for the tabletop of a desk are shown.
Rectangle A=bh
In your answer document, determine how many
square feet of wood will be needed to build the
tabletop if one square represents half-square foot.
Provide proof of your findings by showing your work
and explain your answer.
“Triangle c” A= ½*bh
What do you need to do first?
Break the desk into familiar figures.
Find the area of the “pieces” of the desk in
square units and combine them (add them
together.)
2
“Triangle a” A= 4.5
4.5 + 24 + 9 = 37.5 u
Multiply this result by 0.5 to find the area of
the desk in square feet. 37.5 u2 • 0.5 = 18.75 ft2
Rectangle B A=24
“Triangle c” A= 9
So, 18.75 square feet of wood is needed to build the desk.
Find the Area of the
Complex Figures