Question

geometry
surface area and volume of composite figures
find the surface area of each composite figure. round to the
1.
2.

Explanation:

Step1: Calculate the area of the square base

The base is a square with side length \(6m\). The area of a square is \(A = s^2\), so \(A_{base}=6\times6 = 36m^2\)

Step2: Calculate the lateral surface area of the rectangular part

The rectangular part has two pairs of sides. One pair has dimensions \(6m\times4m\) and the other pair also has dimensions \(6m\times4m\). The lateral surface area of the rectangular part (excluding the top and bottom of the rectangular part which are internal or covered) is \(2\times(6\times4)+2\times(6\times4)= 4\times6\times4=96m^2\)

Step3: Calculate the lateral surface area of the pyramid part

The pyramid has 4 triangular faces. Each triangular face has a base of \(6m\) and a slant height of \(8m\). The area of a triangle is \(A=\frac{1}{2}bh\). The lateral surface area of the pyramid is \(4\times\frac{1}{2}\times6\times8 = 96m^2\)

Step4: Sum up the areas

\(A = 36+96 + 96=228m^2\)

Answer:

\(228m^2\)