Question

guided practice
look at the figure. you are given the lengths of the altitude and the base edge of the square pyramid.
type your answer and then click or tap done.
find the surface area of this square pyramid. (note: first, you will need to use the pythagorean theorem to find the slant height.)
surface areas of pyramids and cones

Explanation:

Step1: Identify base edge length

Base edge = 4 cm (given)

Step2: Calculate base area

Base area = side² = 4² = 16 cm²

Step3: Find slant height

Slant height = 6 cm (given)

Step4: Calculate one triangular face area

Area of 1 triangle = $\frac{1}{2}×base×slant\ height$ = $\frac{1}{2}×4×6$ = 12 cm²

Step5: Calculate lateral surface area

Lateral area = 4×12 = 48 cm²

Step6: Total surface area

Total area = base area + lateral area = 16 + 48 = 64 cm²

Answer:

64 cm²