Question

what is the surface area of the rectangular pyramid below? 11 11 11 a. 242 units² b. 363 units² c. 484 units² d. 1026 units²

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 11$. The area of the base $B$ is given by the formula $B=s^2$. So, $B = 11^2=121$.

Step2: Calculate area of one triangular face

The triangular faces have base $b = 11$ and height $h = 11$. The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. So, $A_{\triangle}=\frac{1}{2}\times11\times11=\frac{121}{2}$.

Step3: Calculate total area of four triangular faces

Since there are 4 triangular faces, the total area of the triangular faces $A_{triangles}=4\times\frac{1}{2}\times11\times11 = 2\times11\times11=242$.

Step4: Calculate surface area

The surface area $SA$ of the rectangular pyramid is the sum of the base - area and the total area of the triangular faces. So, $SA=B + A_{triangles}=121+242 = 363$.

Answer:

B. 363 units$^2$