a First find the number of units the shape covers in the diagram.
B
b Divide the shape into smaller shapes for which you can calculate the area.
A
aAt its longest: 288 feet
At its widest: 256 feet
B
bArea of shape: 59.5 unit^2
Actual Area: 60 928 unit^2
Practice makes perfect
a Let's first identify the length of the vertical and horizontal segments.
To find the overall width and length, we have to add some additional information.
At its longest, the island is 7+2=9 units and at its widest, it is 6+2=8 units. Finally, we will calculate the actual lengths in feet by multiplying these lengths by 32.
At Its Longest:& 9(32)=288 feet
At Its Widest:& 8(32)=256 feet
b To find the area of the shape we will divide it into smaller recognizable shapes for which we have formulas to calculate area.
From the diagram, we can recognize two trapezoids and three rectangles. Let's calculate their different areas and then add them to get the total area.
Area (1):& 1/2(2)(7+9)=16 units^2 [0.9em]
Area (2):& 1/2(1)(5+4)=4.5 units^2 [1.1em]
Area (3):& (5)(3)=15 units^2 [1.1em]
Area (4):& (2)(3)=6 units^2 [1.1em]
Area (5):& (3)(6)=18 units^2
If we add these areas, we get the total area of the shape.
16+4.5+15+6+18=59.5 units^2
The shape is 59.5 square units in total. To convert this into square feet, we have to keep in mind that 1 square unit has two sides of 1 unit. Therefore, when converting 59.5 square units to square feet, we have to multiply 59.5 by 32 twice.
59.5(32)(32)=60 928 feet^2
