Question

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

Explanation:

Step1: Calculate the surface area of the rectangular prism part (excluding the top face which is covered by the pyramid)

The formula for the surface area of a rectangular prism is \(2(lw + lh+wh)\). Here, \(l = 14\) cm, \(w = 10\) cm, \(h = 6\) cm. But we exclude the top - face (\(lw\) part).

$$2(14\times6 + 10\times6)+14\times10$$

$$=2(84 + 60)+140$$

$$=2\times144+140$$

$$=288+140=428$$

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

The two triangular faces with base \(10\) cm and slant height \(12\) cm: Area of a triangle is \(\frac{1}{2}bh\). For two such triangles: \(2\times\frac{1}{2}\times10\times12 = 120\)
The two triangular faces with base \(14\) cm and slant height \(11\) cm: For two such triangles: \(2\times\frac{1}{2}\times14\times11=154\)

Step3: Sum up all the areas

Add the area of the prism (excluding the top) and the areas of the triangular faces: \(428+120 + 154\)

$$428+120+154=702$$

Answer:

702 square centimeters