Bot GPT 4-o mini To find the surface area of a rectangular pyramid, we need to know the dimensions of its base and its height. The rectangular pyramid has a rectangular base with dimensions \( l \) (length) and \( w \) (width), and a height \( h \) (the perpendicular distance from the base to the apex).
In your message, you provided the numbers 26, 25, 14, and 20. It seems like these numbers could represent dimensions, but we need to clarify their meanings.
Let's assume:
- The base dimensions are \( l = 26 \) and \( w = 25 \).
- The height is \( h = 20 \).
- The slant height (the height of the triangular faces) is \( 14 \).
The surface area \( SA \) of a rectangular pyramid can be calculated using the following formula:
\[ SA = lw + \frac{1}{2} \times P \times h_s \]
Where:
- \( lw \) is the area of the base.
- \( P \) is the perimeter of the base.
- \( h_s \) is the slant height of the triangular faces.
Step 1: Calculate the area of the base
\[ lw = 26 \times 25 = 650 \]
Step 2: Calculate the perimeter of the base
\[ P = 2(l + w) = 2(26 + 25) = 2(51) = 102 \]
Step 3: Calculate the area of the triangular faces
The area of one triangular face is given by the formula: \[ \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} \] The base of each triangular face corresponds to one side of the rectangle, and we have two triangular faces for each pair of opposing sides.
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For the two triangles corresponding to the length: \[ \text{Area} = 2 \left(\frac{1}{2} \times 26 \times 14\right) = 26 \times 14 = 364 \]
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For the two triangles corresponding to the width: \[ \text{Area} = 2 \left(\frac{1}{2} \times 25 \times 14\right) = 25 \times 14 = 350 \]
Step 4: Total surface area
Total surface area \( SA \) will be: \[ SA = \text{Area of base} + \text{Area of triangular faces} \] \[ SA = 650 + (364 + 350) \] \[ SA = 650 + 714 = 1364 \]
Final Answer
Therefore, the surface area of the rectangular pyramid is \( 1364 \) square units.
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