← Back to 3. Mathematical Models in Algebra

📝 Area of a rectangle formula (A = LW) (10 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 10 questions available

←Previous Topic:Perimeter of rectangle formula (P = 2L + 2W)📝 Area of a rectangle formula (A = LW)Find rectangle dimensions from perimeter or area:Next Topic→

What is Area of a rectangle formula (A = LW)?

Definition:
The area of a rectangle is the amount of space enclosed within its four sides, calculated by multiplying its length by its width, expressed as $A = L \times W$ , where $L$ is the length and $W$ is the width, and this formula gives the measure of the surface in square units, such as square meters or square feet.

Working:
To find the area, ensure the length and width are in the same unit, multiply them together, and the result is in square units; if you know the area and one dimension, you can find the other by dividing the area by the known dimension, e.g., $L = \frac{A}{W}$ , and this formula works for any rectangle, including squares (where $L = W$ ).

Example:
A rectangular room measures 8 meters by 5 meters; its area is $A = 8 \times 5 = 40$ square meters, meaning the floor space is 40 m $^2$ , which is useful for purchasing flooring materials like tiles or carpet.

Reason:
The area formula is fundamental in many fields, including architecture, agriculture, and interior design, as it helps calculate space for flooring, land measurement, and resource allocation, making it indispensable for planning and construction.

Easy

Medium

Hard

📝 All Area of a rectangle formula (A = LW) MCQs

Q1. A rectangular garden has length 1818 m and width 77 m. Which expression correctly represents its area before calculating the numerical result?

18+7

2(18+7)

18\times7

✅

18^2+7^2

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The area of a rectangle is found by multiplying its length by its width. Therefore, $18\times7$ represents the total number of square meters covered by the garden. The other expressions represent addition, perimeter, or an unrelated calculation.

Q2. Two rectangles have dimensions 1212 cm by 55 cm and 1010 cm by 66 cm. A student claims the first rectangle has greater area because its length is greater. Which conclusion is correct?

A.The first is larger because

12>10

B.The second is larger because

6>5

C.Both have the same area because

12(5)=10(6)

✅

D.There is not enough information

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Comparing only one dimension can be misleading. The first rectangle has area $12\times5=60$ square centimeters, while the second has area $10\times6=60$ square centimeters. Thus, both rectangles have equal areas despite different dimensions.

Q3. A rectangular floor measures 9.59.5 m by 44 m. Tiles cover exactly 11 square meter each. Ignoring cutting and waste, how many square meters of floor must be covered?

A.13.5

B.19

C.38 ✅

D.76

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The floor area is found by multiplying the dimensions: $A=9.5\times4=38$ . Since each tile represents one square meter, 38 square meters must be covered. Adding the dimensions would calculate neither the area nor the required coverage.

Q4. A designer doubles the length of a rectangular banner but keeps its width unchanged. How does the area change?

A.It stays the same

B.It becomes half as large

C.It doubles ✅

D.It becomes four times as large

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Because area depends multiplicatively on both dimensions, changing only the length by a factor of 2 multiplies the entire area by 2. The width remains unchanged, so there is no second factor of 2 to make the area quadruple.

Q5. A rectangle has area $96\text{ cm}^2$ and width 88 cm. A student says its length must be 104104 cm because $96+8=104$ . What should the student do instead?

A.Subtract 8 from 96

B.Divide 96 by 8 ✅

C.Multiply 96 by 8

D.Divide 8 by 96

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since the area equals length multiplied by width, the unknown length can be found by reversing multiplication. Dividing the area by the known width gives $96\div8=12$ cm. Adding dimensions confuses area with perimeter.

Q6. A rectangular playground is 3030 m long and 2020 m wide. A path occupies a rectangular region measuring 3030 m by 33 m along one edge. What area remains for the playground surface?

A.510

\text{m}^2

✅

B.600

\text{m}^2

C.690

\text{m}^2

D.5100

\text{m}^2

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The original playground has area $30\times20=600\text{ m}^2$ . The path has area $30\times3=90\text{ m}^2$ . Subtracting the path from the original region gives $600-90=510\text{ m}^2$ remaining.

Q7. A rectangular sheet is 1616 cm by 99 cm. It is cut into two rectangles, each 88 cm by 99 cm. Which statement best evaluates the student's claim that cutting the sheet reduces its total area?

A.Correct, because both dimensions decrease

B.Correct, because cutting always reduces area

C.Incorrect, because

2(8\times9)=16\times9

✅

D.Incorrect, because perimeter determines area

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Each smaller rectangle has area $8\times9=72\text{ cm}^2$ . Together they cover $144\text{ cm}^2$ , exactly the original $16\times9=144\text{ cm}^2$ . Cutting changes the pieces but does not remove material, so total area remains unchanged.

Q8. A student calculates the area of a 1414 cm by 66 cm rectangle as $40\text{ cm}^2$ , explaining that $14+6+14+6=40$ . What error did the student make?

A.They calculated a perimeter instead of an area ✅

B.They multiplied the dimensions incorrectly

C.They used the wrong unit conversion

D.They should have squared both dimensions

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The calculation $14+6+14+6=40$ adds all four sides, so it finds the perimeter, measured in centimeters. Area requires multiplying length by width: $14\times6=84\text{ cm}^2$ . The student's arithmetic is correct for the wrong quantity.

Q9. A rectangular room has fixed area $120\text{ m}^2$ . If its length changes from 1010 m to 1515 m while the area remains fixed, what must happen to its width?

A.It increases from 12 m to 18 m

B.It decreases from 12 m to 8 m ✅

C.It remains 12 m

D.It decreases from 10 m to 8 m

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Initially, the width is $120\div10=12$ m. After the length becomes 15 m, the width must be $120\div15=8$ m to preserve the same area. This demonstrates that when area is fixed, increasing one dimension requires decreasing the other.

Q10. A farmer wants to enclose a rectangular region with area $400\text{ m}^2$ . Which dimensions use the greatest length while still producing exactly this area?

A.20 m by 20 m

B.25 m by 16 m

C.40 m by 10 m

D.80 m by 5 m ✅

💡 Difficulty: easy | ✅ Correct: D

📖 Explanation: All choices produce $400\text{ m}^2$ , but the question asks for the greatest length. Comparing the lengths $20,25,40,$ and $80$ , the 80 m by 5 m rectangle has the greatest length while maintaining the required area. This requires separating area from shape.

🔗 Related Topics (MCQs)

📝 How Use a Problem Solving Strategy MCQs 📝 How to Approach word problems MCQs 📝 How to Use a problem solving strategy for word problems MCQs 📝 How to Solve number problems MCQs 📝 Translate English sentences into algebraic equations MCQs

←Previous Topic:Perimeter of rectangle formula (P = 2L + 2W)📝 Area of a rectangle formula (A = LW)Find rectangle dimensions from perimeter or area:Next Topic→