Question
Find the surface area of the rectangle base pyramid. (hint 90 cm = 0.9m)
Base edge: 90 cm
Base perimeter: 1.2cm
Slanted Height: 3.82m
Slanted Height: 3.8m
A. 15.7m^2
B. 1.08m^2
C. 7.98m^2
D. 9.06m^2
Base edge: 90 cm
Base perimeter: 1.2cm
Slanted Height: 3.82m
Slanted Height: 3.8m
A. 15.7m^2
B. 1.08m^2
C. 7.98m^2
D. 9.06m^2
Answers
GPT-4o mini
To find the surface area of a rectangular base pyramid, we need to calculate the area of the base and the area of the triangular faces.
1. **Base Area**: The base of the pyramid is a square since the problem talks about a "rectangle base pyramid" but provides a single base edge (90 cm). First, we must convert that measurement to meters.
- Base edge = 90 cm = 0.9 m
- Area of the base (A_base) = (base edge)² = (0.9 m)² = 0.81 m².
2. **Triangular Faces**: The pyramid has 4 triangular faces. We will calculate the area of one triangular face and then multiply that by 4.
Each triangular face has:
- Base = base edge = 0.9 m
- Height = slanted height = 3.8 m
- Area of one triangle (A_triangle) = (1/2) × base × height
\[
A_triangle = \frac{1}{2} \times 0.9 \, m \times 3.8 \, m = \frac{1}{2} \times 3.42 \, m^2 = 1.71 \, m^2
\]
Since there are 4 triangular faces:
\[
Total \, area \, of \, triangular \, faces = 4 \times A_triangle = 4 \times 1.71 \, m^2 = 6.84 \, m^2
\]
3. **Total Surface Area**: The total surface area (SA) of the pyramid is the area of the base plus the area of the triangular faces.
\[
SA = A_{base} + Total \, area \, of \, triangular \, faces = 0.81 \, m^2 + 6.84 \, m^2 = 7.65 \, m^2
\]
After double-checking the calculation, I see we came to a total surface area of \( 7.65 \, m^2 \). However, since the answer choices provided do not include this specific answer, I will check once more to see what may have been misunderstood:
- After verifying the lengths and conversions, it appears that the possible answers you provided are either illustrating a different pyramid configuration or there may have been a misunderstanding in measurements/shape qualms.
None of the answer choices match my final calculation of 7.65 m², but based on the closest usable option, it seems classified near C (7.98 m²).
Thus, if asked for the best approximation based on choices provided, the selected answer would be:
\[
**C. 7.98m²**
\]
1. **Base Area**: The base of the pyramid is a square since the problem talks about a "rectangle base pyramid" but provides a single base edge (90 cm). First, we must convert that measurement to meters.
- Base edge = 90 cm = 0.9 m
- Area of the base (A_base) = (base edge)² = (0.9 m)² = 0.81 m².
2. **Triangular Faces**: The pyramid has 4 triangular faces. We will calculate the area of one triangular face and then multiply that by 4.
Each triangular face has:
- Base = base edge = 0.9 m
- Height = slanted height = 3.8 m
- Area of one triangle (A_triangle) = (1/2) × base × height
\[
A_triangle = \frac{1}{2} \times 0.9 \, m \times 3.8 \, m = \frac{1}{2} \times 3.42 \, m^2 = 1.71 \, m^2
\]
Since there are 4 triangular faces:
\[
Total \, area \, of \, triangular \, faces = 4 \times A_triangle = 4 \times 1.71 \, m^2 = 6.84 \, m^2
\]
3. **Total Surface Area**: The total surface area (SA) of the pyramid is the area of the base plus the area of the triangular faces.
\[
SA = A_{base} + Total \, area \, of \, triangular \, faces = 0.81 \, m^2 + 6.84 \, m^2 = 7.65 \, m^2
\]
After double-checking the calculation, I see we came to a total surface area of \( 7.65 \, m^2 \). However, since the answer choices provided do not include this specific answer, I will check once more to see what may have been misunderstood:
- After verifying the lengths and conversions, it appears that the possible answers you provided are either illustrating a different pyramid configuration or there may have been a misunderstanding in measurements/shape qualms.
None of the answer choices match my final calculation of 7.65 m², but based on the closest usable option, it seems classified near C (7.98 m²).
Thus, if asked for the best approximation based on choices provided, the selected answer would be:
\[
**C. 7.98m²**
\]