Question

find the surface area of the square pyramid. 377 sq. cm 441 sq.cm 389 sq. cm 429 sq. cm

Explanation:

Step1: Calculate base area

The base is a square with side length $a = 11$ cm. The area of the base $B=a^{2}=11^{2}=121$ $cm^{2}$.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. Here, the base of the triangular face $b = 11$ cm and the slant - height $h = 14$ cm. So, $A_{\triangle}=\frac{1}{2}\times11\times14 = 77$ $cm^{2}$.

Step3: Calculate total area of 4 triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{\triangle}=4\times77 = 308$ $cm^{2}$.

Step4: Calculate surface area of the pyramid

The surface area $SA$ of a square - pyramid is the sum of the base area and the area of the 4 triangular faces. So, $SA=B + A_{triangles}=121+308 = 429$ $cm^{2}$.

Answer:

D. 429 sq. cm