What is the area of the figure below? (1 point) 5 in. 3 in. 12 in. 18 in.
30 in.
36 in.
60 in.
The Correct Answer and Explanation is:
To find the area of the parallelogram in the figure, we use the formula for the area of a parallelogram: Area=base×height\text{Area} = \text{base} \times \text{height}
From the image:
- The base is given as 12 inches.
- The height (perpendicular distance between the bases) is 3 inches.
Step-by-step Calculation:
Area=12 inches×3 inches=36 square inches\text{Area} = 12 \, \text{inches} \times 3 \, \text{inches} = 36 \, \text{square inches}
Therefore, the correct answer is:
36 in²
Explanation
The figure in question is a parallelogram, a four-sided polygon with opposite sides that are parallel and equal in length. Unlike rectangles, parallelograms do not necessarily have right angles, so we must rely on a different approach to calculate the area.
The formula for the area of a parallelogram is: Area=base×height\text{Area} = \text{base} \times \text{height}
It’s important to note that the height used in this formula is not the slanted side or the length of the side inclined at an angle. Instead, it is the perpendicular height from the base to the top side, which essentially measures how “tall” the shape is when standing on its base.
In the given figure:
- The base of the parallelogram is clearly labeled as 12 inches.
- A dotted line representing the height is marked as 3 inches, perpendicular to the base.
Although one side of the parallelogram is marked as 5 inches, that is the length of the slanted side and not used for calculating area.
Multiplying the base by the height: 12 inches×3 inches=36 square inches12 \, \text{inches} \times 3 \, \text{inches} = 36 \, \text{square inches}
This gives us the area. Among the answer choices (18, 30, 36, and 60 square inches), 36 in² is correct.
This question tests understanding of geometric formulas and recognizing the correct components (base and perpendicular height) to use when calculating the area of a parallelogram.
