Answer :
To solve this problem, we need to accurately identify the units for each component in the formula for surface area of a geometric shape, given as [tex]\( SA = (p \cdot h) + 2B \)[/tex]. Let's break down the formula step-by-step:
1. Perimeter (p):
The perimeter of a geometric shape is the total distance around the shape. Perimeter is a linear measurement. Therefore, the unit for perimeter is typically given in inches (in).
2. Height (h):
Height is also a linear measurement, representing the vertical distance from the base to the top of the shape. The unit for height is also in inches (in).
3. Area of the base (B):
Area represents a measure of the total size of a 2-dimensional surface. The unit for area is in square inches (in²), as it is measured in two dimensions.
Combining these insights:
- The perimeter [tex]\(p\)[/tex] is in inches (in).
- The height [tex]\(h\)[/tex] is in inches (in).
- The area of the base [tex]\(B\)[/tex] is in square inches (in²).
Thus, the correct answer is:
A. in; in²; in
1. Perimeter (p):
The perimeter of a geometric shape is the total distance around the shape. Perimeter is a linear measurement. Therefore, the unit for perimeter is typically given in inches (in).
2. Height (h):
Height is also a linear measurement, representing the vertical distance from the base to the top of the shape. The unit for height is also in inches (in).
3. Area of the base (B):
Area represents a measure of the total size of a 2-dimensional surface. The unit for area is in square inches (in²), as it is measured in two dimensions.
Combining these insights:
- The perimeter [tex]\(p\)[/tex] is in inches (in).
- The height [tex]\(h\)[/tex] is in inches (in).
- The area of the base [tex]\(B\)[/tex] is in square inches (in²).
Thus, the correct answer is:
A. in; in²; in
