What is the area of the rectangle below? 10 13 A. 23 sq. units B. 46 sq. units C. 130 sq. units D. 65 sq. units
The correct answer is C. 130 sq. units.
To determine the area of the rectangle shown in the image, we must use the fundamental formula for the area of a rectangle. The area represents the total two dimensional space enclosed within the boundaries of the shape. It is typically measured in square units, such as square inches, square meters, or in this case, generic “square units”.
The formula to calculate the area of any rectangle is:
Area = Length × Width
In the provided diagram, the rectangle has two given side lengths. The horizontal side, which we can consider the length, is labeled as 13 units. The vertical side, which we can consider the width or height, is labeled as 10 units. The small square symbols in each corner of the figure indicate that all four interior angles are right angles (90 degrees), which is a defining characteristic of a rectangle.
Now, we can substitute the given values into the area formula:
Length = 13 units
Width = 10 units
Area = 13 × 10
Performing the multiplication gives us:
Area = 130 square units
This result means that 130 squares, each with sides of one unit, could fit perfectly inside this rectangle.
Let’s examine the other options to understand why they are incorrect.
Option A: 23 sq. units is incorrect. This value is obtained by adding the length and the width (13 + 10 = 23). This calculation does not represent the area of the rectangle.
Option B: 46 sq. units is also incorrect. This value represents the perimeter of the rectangle. The perimeter is the total distance around the outside of a shape. It is calculated by adding all the side lengths together: Perimeter = 2 × (Length + Width). For this rectangle, the perimeter would be 2 × (13 + 10) = 2 × 23 = 46 units. The question specifically asks for the area, not the perimeter.
Option D: 65 sq. units is incorrect. This value would be the area of a triangle with a base of 13 and a height of 10, since the formula for a triangle’s area is (Base × Height) / 2. This would be (13 × 10) / 2 = 130 / 2 = 65 square units. However, the shape shown is clearly a rectangle, not a triangle.
Therefore, the only correct calculation for the area of the given rectangle is 13 multiplied by 10, which equals 130 square units.
