Answer:
i tried but i came up with the answer 274 square centimeters
Answer:
274 square units
Step-by-step explanation:
A frustum of a regular square pyramid is the portion of the pyramid that remains after a smaller, similar pyramid is removed from the top.
This results in a figure with two parallel congruent bases (one smaller than the other) connected by lateral faces, which are trapezoidal.
The total surface area of any frustum is obtained by adding the area of the two parallel congruent bases to the lateral surface area.
The parallel congruent bases of the frustum of a regular square pyramid are both square. The area of a square is the square of its side length. Given that the top edge of the frustum is 5 and the bottom edge is 9, the combined area of the parallel congruent bases is:
[tex]\textsf{Area of bases}=5^2+9^2\\\\ \textsf{Area of bases}=25+81\\\\\textsf{Area of bases}=106\; \sf square\;units[/tex]
The lateral surface area of any frustum of a regular square pyramid is made up of four congruent isosceles trapezoids. The area of a trapezoid is half the sum of its two parallel bases multiplied by the height.
In this case, the two parallel bases are 5 and 9, and the height of the trapezoids is the slant height of the frustum, which is 6. Therefore, the lateral surface area of the frustum is:
[tex]\textsf{Lateral Surface Area}=4 \cdot \dfrac{(5+9)}{2} \cdot 6\\\\\\\textsf{Lateral Surface Area}=4 \cdot \dfrac{14}{2} \cdot 6\\\\\\\textsf{Lateral Surface Area}=4 \cdot 7 \cdot 6\\\\\\\textsf{Lateral Surface Area}=168\; \sf square\;units[/tex]
Finally, to find the total surface area of the frustum, sum the area of the bases and the lateral surface area:
[tex]\textsf{Total surface area}=106+168\\\\\textsf{Total surface area}=274\; \sf square\;units[/tex]
Therefore, the total surface area of the frustum of a regular square pyramid is:
[tex]\LARGE\boxed{\boxed{274\; \sf square\;units}}[/tex]
