a The area of a parallelogram is the base b multiplied by its height h.
B
b The area of a trapezoid is the sum of the parallel sides multiplied by its height and finally divided by 2.
C
c Use the labeled sides to find the length of the unlabeled sides.
D
d This is actually a trapezoid with a rectangle cut out.
A
aPerimeter: 52 cm
Area: 144 cm^2
B
bPerimeter: 114.67 m
Area: 696.7 m^2
C
cPerimeter: 48 cm
Area: 72 cm^2
D
dPerimeter: 58 feet
Area: 130 feet^2
Practice makes perfect
a The perimeter of any figure is the sum of all of its sides. In this case, all sides have been given so we can calculate the perimeter directly.
Perimeter: 10+10+16+16=52 cmThe area of a parallelogram is the base b multiplied by its height h. Let's identify these dimensions in the figure.
Having identified the base and height, we can calculate the area.
Area: ( 9)( 16) = 144 cm^2
b Just like in Part A, we calculate the perimeter of the trapezoid by adding all of the sides which have been given. Notice that the height is not a part of the perimeter.
Perimeter: 21+25+24+44.67=114.67 mThe area of a trapezoid is the sum of the parallel sides b_1 and b_2 multiplied by its height h and divided by 2. Let's identify these dimensions in our figure.
Having identified the parallel sides and height of the trapezoid, we can calculate the area.
c Like in previous parts A and B, we calculate the perimeter of the trapezoid by adding all of its sides. Using the information in the diagram, we can find the length of the unknown sides.
To find the perimeter, we will add the red lengths from the diagram.
Perimeter: 12+2+3...+7+2-3=48 cm
To determine the area, we will cut up the figure into three rectangles.
The area of a rectangle is the product of its width and length. With this, we can calculate the total area of the figure by adding the areas of the individual rectangles.
A=(2)(12)+(7)(6)+(2)(3)=72 cm^2
d All side lengths have been given and therefore, we can calculate the perimeter directly by adding them.
Perimeter: 10+4+...+10+23=58 feetExamining the diagram, we see that this is actually a trapezoid with a rectangle cut out of the top. Therefore, we can calculate the figures area by determining the area of the trapezoid and then subtract the area of the cutout. Let's identify the trapezoid's parallel sides b_1 and b_2 as well as the height h.
Having identified the trapezoid's parallel sides and height, we can calculate its area and then subtract the cutout.
