Final answer:
To draw the pyramid, sketch a base square with 25.7 m sides and slant heights of 27.2 m connecting each side's midpoint to the apex. Use the Pythagorean theorem to confirm the accurate height among the given options.
Step-by-step explanation:
The question asks you to sketch and label a tropical pyramid with 4 congruent triangular faces, a base length of 25.7 m, and to consider various heights for the pyramid. To depict this pyramid, draw a square for the base with each side measuring 25.7 m. Then, from the midpoint of each base side, draw a line upward representing the slant height, which is 27.2 m. These lines should meet at a point above the center of the base square, creating the apex of the pyramid. The various heights presented (10.6 m, 13.5 m, 17.1 m, and 21.3 m) are vertical lines from the apex perpendicular to the base.
Using the pythagorean theorem, you can verify which height is correct. The slant height and half the base of the pyramid form a right-angled triangle with the height. Using these values, you can calculate the correct height of the pyramid.