Question

surface area of composite figures
what is the total surface area of the solid?
982 square centimeters
702 square centimeters
558 square centimeters
842 square centimeters

Explanation:

Step1: Calculate the surface area of the rectangular prism part (excluding the top face)

The formula for the surface area of a rectangular prism is \(2(lw + lh+ wh)\). Here, we exclude the top - face (the face where the prism and the pyramid are joined).
The dimensions of the prism are \(l = 14\space cm\), \(w = 10\space cm\), \(h = 6\space cm\).
The area of the four lateral faces and the bottom face: \(2\times(14\times6 + 10\times6)+14\times10\)

$$
LATEXBLOCK0
$$

Step2: Calculate the surface area of the triangular faces of the pyramid

The pyramid has two types of triangular faces.

• For the triangles with base \(b = 14\space cm\) and height \(h = 11\space cm\): The area of a triangle is \(A=\frac{1}{2}bh\). The area of two such triangles is \(2\times\frac{1}{2}\times14\times11=154\space cm^{2}\)
• For the triangles with base \(b = 10\space cm\) and height \(h = 12\space cm\): The area of two such triangles is \(2\times\frac{1}{2}\times10\times12 = 120\space cm^{2}\)

Step3: Calculate the total surface area

Add the surface area of the prism (excluding the top) and the surface area of the pyramid's triangular faces.

$$428+154 + 120=702\space cm^{2}$$

Answer:

702 square centimeters