Question

What is the surface area of this composite solid?

square feet

Answer 1

let's take a peek

we really have a rectangular prism below a square pyramid.

the prism has a front, back, left and right of a rectangle 2x11 .

its bottom or base is an 11x11 square.

the pyramid 4 triangles, each one has a base of 11 and a height of 7.

`\bf \stackrel{\textit{front, back, left, right}}{4(2\cdot 11)}~~+~~\stackrel{\textit{base}}{(11\cdot 11)}~~+~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(11)(7) \right]} \\\\\\ 88+121+154\implies 363`

Answer 2

The surface area of composite solid = 363 ft²

Explanation:

Points to remember

Area of rectangle = Length * Breadth

Area of triangle = bh/2

Where b - Base and h - Height

To find the surface area of composite solid

Surface area = Base area + side area + area of 4 triangles

= (11 * 11) + 4(11 * 2) + 4(11 * 7)/2

= 121 + 88 + 154

= 363 ft²

Therefore the surface area of composite solid = 363 ft²