Area and Perimeter Word Problems

Area and Perimeter Word Problems
• Page 1
1.
What is the area of a parallelogram, if its base is 9 ft and its height is 14 ft?
 a. 46 ft2 b. 126 ft2 c. 46 ft d. 63 ft2

Solution:

Area of a parallelogram = base × height
[Formula.]

= 9 × 14
[Substitute the values of base and height.]

= 126
[Multiply.]

So, area of the parallelogram is 126 ft2.

2.
Find the area of the colored region in the figure.

 a. 22 cm2 b. 20 cm2 c. 28 cm2 d. 26 cm2

Solution:

From the figure, the colored region is a parallelogram BEDF.

The base length of the parallelogram BEDF = 7 cm
[From the figure.]

The height of the parallelogram BEDF = 4 cm
[From the figure.]

Area of the parallelogram BEDF = base x height
[Formula.]

= 7 x 4
[Substitute the values.]

= 28

So, area of the colored region = area of the parallelogram BEDF = 28 cm2.

3.
What is the area of ΔABC in the figure, if the height of ΔABC is 3 times the height of ΔDBC and area of ΔDBC is 40 inch2?

 a. 115 inch2 b. 120 inch2 c. 110 inch2 d. None of the above

Solution:

Area of a triangle = 1 / 2 x base x height
[Formula.]

Let h be the height of ΔDBC

Area of ΔDBC = 1 / 2 x BC x h.

Height of ΔABC = 3 times the height of ΔDBC = 3h.

Area of ΔABC = 1 / 2 x BC x 3h

= 3 x (12 x BC x h)

= 3 x (Area of ΔDBC)

Area of ΔABC = 3 x 40 = 120 inch2.

4.
The perimeter of an equilateral triangle is 36 yd. What is the length of each side of the triangle?
 a. 108 yd b. 12 yd c. 3 yd d. 9 yd

Solution:

In an equilateral triangle, all sides are equal.

So, the perimeter of an equilateral triangle = 3 × measure of each side.

36 = 3 × measure of each side
[Substitute the values.]

36 / 3 = 3 × measure of each side3
[Divide each side by 3.]

12 = measure of each side
[Simplify.]

So, the measure of each side of the equilateral triangle is 12 yd.

5.
Which of the figures have equal areas?

 a. Figure 1 & 3 b. Figure 1 & 2 c. Figure 2 and 3 d. Figure 1,2 & 3

Solution:

Figure 1 represents a parallelogram with its base length 4 units and height 2 units.

Area of the parallelogram = base × height = 4 × 2 = 8 square units.

Figure 2 represents a rectangle of length 4 units and width 2 units.

Area of the rectangle = length × width = 4 × 2 = 8 square units.

Figure 3 represents a triangle with a base length of 6 units and a height of 3 units.

Area of the triangle = 1 / 2 × base × height = 1 / 2 × 6 × 3 = 9 square units.

So, the parallelogram in figure 1 and the rectangle in figure 2 have equal areas.

6.
John spent $\frac{2}{3}$ of an hour watching a movie and $\frac{1}{6}$ of an hour cleaning his room. What fraction of an hour did he spend in both watching the movie and cleaning his room?
 a. $\frac{3}{9}$ b. $\frac{1}{3}$ c. $\frac{2}{3}$ d. $\frac{5}{6}$

7.
Which two parallelograms have same area but different perimeters?

 a. Figure 1 and Figure 2 b. Figure 2 and Figure 4 c. Figure 1 and Figure 3 d. Figure 3 and Figure 4

Solution:

Area of a parallelogram = Base × Height Perimeter of a parallelogram = 2 × (Base + Height)

Area = 5 × 4 = 20 sq.units Perimeter = 2 × (5 + 4) = 18 units

Area = 6 × 3 = 18 sq.units Perimeter = 2 × (6 + 3) = 18 units

Area = 6 × 2 = 12 sq.units Perimeter = 2 × (6 + 2) = 16 units

Area = 4 × 3 = 12 sq.units Perimeter = 2 × (4 + 3) = 14 units

Therefore, parallelograms in Figure 3 and Figure 4 have same area but different perimeters.

8.
Which statement about the figures is true?

 a. Both the figures have the same area. b. Both the figures have the same length. c. Both the figures have the same perimeter. d. Both the figures have the same width.

Solution:

Parallelogram in Figure 1 has a base of 6 units and a height of 2 units.

Parallelogram in Figure 2 has a base of 4 units and a height of 3 units.

Area of a parallelogram = Base × Height Perimeter of a parallelogram = 2 × (Base + Height)

Area = 6 × 2 = 12 sq.units Perimeter = 2 × (6 + 2) = 16 units

Area = 4 × 3 = 12 sq.units Perimeter = 2 × (4 + 3) = 14 units

Therefore, the statement 'Both the figures have the same area' is true.

9.
Which of the following is true for a right triangle and a rectangle having equal bases and equal heights?
 a. The perimeter of the triangle is equal to the perimeter of the rectangle b. The area of the triangle is equal to the area of the rectangle c. The area of the triangle is half the area of the rectangle d. The area of the rectangle is half the area of the triangle

Solution:

Let the length of the common base be b

Let the length of the common height be h

Area of the rectangle = b × h

Area of the triangle = 12 × b × h

= 12 × Area of the rectangle

So, the area of the triangle is half the area of the rectangle.

10.
A parallelogram and a rectangle have equal bases and equal heights. What is the area of the rectangle, if the area of the parallelogram is 44 cm2?
 a. 44 cm2 b. 11cm2 c. 22 cm2 d. 88 cm2

Solution:

If the base and height of the parallelogram and the rectangle are same, then the area of the parallelogram is same as that of rectangle.

So, the area of the rectangle = the area of the parallelogram = 44 cm2.