# Lesson Worksheet: Areas of Rectangles and Squares Mathematics • 6th Grade

In this worksheet, we will practice finding the areas of rectangles and squares using a formula with fractions and decimals and solving real-life problems.

**Q2: **

Given that is a rectangle of area 1,389.6 cm^{2}, find the area of figure .

**Q6: **

The size of youth soccer fields depends on the age group of the players. Use the table to determine the difference between the area of a soccer field for under 14s compared to the field for under 12s.

Age Group | Under 10s | Under 12s | Under 14s |
---|---|---|---|

Field Length (Yards) | 70 | 80 | 100 |

Field Width (Yards) | 40 | 50 | 60 |

**Q7: **

Michael wants to pave a section of his yard that is 16 m long and 3 m wide. If paving one square meter will cost 9 LE, calculate the total cost.

**Q8: **

Jenniferβs rectangular patio is 45 feet long and covers 1,575 square feet. She wants to fence all but one of the shorter sides. How much fencing does she need?

**Q9: **

A 2-inch-wide rectangular frame surrounds a painting that is 9 inches wide and 12 inches tall. What is the area of the frame?

**Q10: **

A family is planning to have a rectangular swimming pool in their backyard. The pool will be 19 ft by 13 ft. Given that they also plan on having a ceramic walkway around the pool, which should be 8 ft wide, determine the area of the walkway.

**Q11: **

A gymnasium floor that is 50 ft wide and 84 ft long needs to be refinished. If the cost for refinishing is $14 per square foot, determine the total cost.

**Q12: **

If the length of every side of a rectangle is increased by 6 units, would its area increase by 36 square units?

- AYes
- BNo

**Q13: **

A rectangle with an area of 196 square feet is 4 times as long as it is wide. Find its length and width.

- Alength = 7 ft, width = 1.8 ft
- Blength = 78.4 ft, width = 19.6 ft
- Clength = 56 ft, width = 14 ft
- Dlength = 98 ft, width = 24.5 ft
- Elength = 28 ft, width = 7 ft

**Q14: **

The figure represents two shelves used to display toys in a store. Shelf 1 is large enough for 4 toys. For every additional square foot of area a shelf has, it can hold one more toy. How many toys can shelf 2 hold?

**Q15: **

The student committee in a school are building a stage in the gym for the upcoming prom. The stage is 16 feet long and 10 feet wide, and the gym is 30 feet by 27 feet. How many square feet of open space will be left after the stage is completed?

**Q16: **

Sophiaβs garden is 14 by 15 feet. If she extends the length of each side by 7 feet, by how many square feet will the area increase?

**Q17: **

In the figure, . Given that the areas of the squares
and are 324 cm^{2} and
1,314 cm^{2} respectively, find the length of
.

**Q18: **

Given that three-quarters of the area of a square is m^{2}, calculate its side length.

- A m
- B m
- C m
- D m

**Q19: **

The length of a rectangle is 13 cm more than its width.
The rectangleβs area is 48 cm^{2}. What is its length?

**Q20: **

Given that the area of the rectangle is 56 cm^{2},
find the length of .

**Q21: **

Given that the length of a rectangle is 2 times its width, and its perimeter is 114 cm, find its area.

**Q22: **

Find the missing side of the rectangle in centimeters, knowing that its area is 0.285 m^{2}.

**Q23: **

The width of a rectangle is of its length. If the length of the rectangle is 14 cm, find the width and area of the rectangle.

- Awidth cm, area cm
^{2} - Bwidth cm, area cm
^{2} - Cwidth cm, area cm
^{2} - Dwidth cm, area cm
^{2} - Ewidth cm, area cm
^{2}

**Q24: **

David wants to carpet a room measuring 9 by 12 meters. Determine the amount of carpet needed.

**Q25: **

What is the area of a rectangle of width 7 and length 25?