Easy GRE Area Questions Practice Questions

Concept Explanation

Area measures the size of a two-dimensional surface and is expressed in square units. For the GRE, you must be comfortable calculating the space inside basic geometric shapes such as rectangles, triangles, circles, and trapezoids. These Easy GRE Area Questions typically require the direct application of a specific formula without complex multi-step reasoning. Understanding these fundamentals is a critical step in your GRE Prep journey. Below are the primary formulas used in these problems:

When approaching these questions, always ensure your units are consistent. For more foundational practice, you might find Free GRE Practice Questions helpful for building speed and accuracy. Many students use tools like the AI Question Generator to create variations of these area problems to ensure they have the formulas memorized and ready for test day.

Solved Examples

Review these three examples to see how to apply area formulas in a testing context.

1. Example 1: Rectangle Area
   A rectangular rug has a length of 8 feet and a width of 5 feet. What is the area of the rug in square feet?
   Solution:

   1. Identify the formula for the area of a rectangle: $A = l \ \times w$.

   2. Plug in the given values: $A = 8 \ \times 5$.

   3. Calculate the result: $A = 40$.

   4. The area is 40 square feet.

2. Example 2: Circle Area
   A circular garden has a diameter of 10 meters. What is the area of the garden in terms of $\pi$?
   Solution:

   1. Determine the radius from the diameter. Radius $r = \ \frac{d}{2} = \ \frac{10}{2} = 5$.

   2. Recall the formula for the area of a circle: $A = \pi r^2$.

   3. Substitute the radius: $A = \pi (5)^2$.

   4. Simplify: $A = 25\pi$.

   5. The area is $25\pi$ square meters.

3. Example 3: Triangle Area
   A right triangle has a base of 6 inches and a height of 4 inches. Find its area.
   Solution:

   1. Use the triangle area formula: $A = \ \frac{1}{2}bh$.

   2. Insert the known values: $A = \ \frac{1}{2}(6)(4)$.

   3. Multiply the base and height: $6 \ \times 4 = 24$.

   4. Take half of the product: $\ \frac{1}{2} \ \times 24 = 12$.

   5. The area is 12 square inches.

Practice Questions

1. A square has a perimeter of 24 units. What is the area of the square?

2. The area of a rectangle is 48 square centimeters. If the width is 6 centimeters, what is the length?

3. A circle has a radius of 7. What is its area? (Assume $\pi \approx \ \frac{22}{7}$)

4. A triangle has an area of 15 square meters and a base of 5 meters. What is the height of the triangle?

5. A trapezoid has parallel bases of 4 cm and 10 cm, and a height of 5 cm. Calculate its area.

6. If the circumference of a circle is $12\pi$, what is the area of the circle?

7. A rectangular floor measures 12 feet by 15 feet. If tiles cost $4 per square foot, how much will it cost to cover the floor?

8. A square is inscribed in a circle with a radius of 5. What is the area of the square?

9. The area of a circle is $64\pi$. What is its diameter?

10. A right triangle has legs of length 8 and 15. What is its area?

Answers & Explanations

1. 36: A square has four equal sides. If the perimeter is 24, each side $s = \ \frac{24}{4} = 6$. The area is $s^2 = 6^2 = 36$.

2. 8 cm: Area of a rectangle $A = l \ \times w$. Given $48 = l \ \times 6$. Dividing both sides by 6 gives $l = 8$.

3. 154: Area $A = \pi r^2$. Using $r = 7$ and $\pi \approx \ \frac{22}{7}$, we get $A = \ \frac{22}{7} \ \times 7^2 = \ \frac{22}{7} \ \times 49 = 22 \ \times 7 = 154$.

4. 6 m: $A = \ \frac{1}{2}bh$. Substituting the values, $15 = \ \frac{1}{2}(5)(h)$. Multiply both sides by 2 to get $30 = 5h$. Divide by 5 to find $h = 6$.

5. 35 cm²: Area of a trapezoid $A = \ \frac{b_1 + b_2}{2}h$. Substituting: $A = \ \frac{4 + 10}{2} \ \times 5 = \ \frac{14}{2} \ \times 5 = 7 \ \times 5 = 35$.

6. 36π: Circumference $C = 2\pi r$. Given $12\pi = 2\pi r$, so $r = 6$. Area $A = \pi r^2 = \pi (6^2) = 36\pi$.

7. $720: First find the area: $12 \ \times 15 = 180$ square feet. The total cost is 180 x $4 = $720.

8. 50: The diagonal of the square is the diameter of the circle. Diameter $d = 2r = 10$. For a square, Area $A = \ \frac{d^2}{2}$ (derived from the Pythagorean theorem). $A = \ \frac{10^2}{2} = \ \frac{100}{2} = 50$.

9. 16: Area $A = \pi r^2 = 64\pi$, so $r^2 = 64$ and $r = 8$. Diameter $d = 2r = 16$.

10. 60: In a right triangle, the legs serve as the base and height. $A = \ \frac{1}{2}(8)(15) = 4 \ \times 15 = 60$.

1. If the side of a square is doubled, what happens to its area?

• AIt doubles
• BIt triples
• CIt quadruples
• DIt stays the same

Frequently Asked Questions

What is the difference between area and perimeter?

Area measures the total space inside a shape's boundaries in square units, while perimeter measures the total distance around the outside edge of the shape in linear units.

Do I need to memorize the value of pi for the GRE?

Most GRE questions leave $\pi$ in the answer choices, but you should know it is approximately 3.14 or $\ \frac{22}{7}$ for questions requiring a numerical estimate.

How do I find the area of an irregular shape on the GRE?

You can usually find the area of an irregular shape by decomposing it into smaller, standard shapes like rectangles and triangles and then adding their individual areas together.

What happens to the area of a rectangle if only the length is doubled?

If only one dimension of a rectangle is doubled, the total area of the rectangle will also double, as seen in the formula $A = (2l) \ \times w = 2(lw)$.

Can area ever be a negative number?

No, area represents a physical extent of space and must always be a non-negative value; in geometry problems, it is strictly positive.

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