Question

A monument in a park is shaped like a square pyramid. The dimensions are shown in the net. What is the surface area of the monument, including the base?

Answer 1

16 square meters

Explanation

Surface area is the amount of space covering the outside of a three-dimensional shape. for a square pyramid we have:

the total surface area is the sum of 4 triangles and the square,so

surface area= area of square+4 times area of the triangle

$\begin{gathered} Surafce\text{ area=\lparen side*side\rparen+4\lparen}\frac{1}{2}(side*slant)) \\ s.a=side^2+2(side*slant) \end{gathered}$

so

Step 1

a)let

$\begin{gathered} side=\text{ 2 m} \\ slant\text{ heigth = 3 m} \end{gathered}$

b) now, replace in the formula

$\begin{gathered} s.a.=side^2+2(side*slant) \\ s.a=(2\text{ m\rparen}^2+2(2m*3m) \\ s.a.=(4+12)m^2 \\ s.a=16\text{ m}^2 \end{gathered}$

so, the answer is 16 square meters

I hope this helps you