Question

Find the surface area of each solid. All quadrilaterals are rectangles, and all given measurements are in centimeters. Round your answers to the nearest 0.1cm^2The base is a regular hexagon with apothem a = 12.1, side s = 14, and height h = 7.

Answer 1

1604.4 sq. cm.

Explanation:

The base of the solid is a regular hexagon.

A regular hexagon can be divided into 6 equilateral triangles.

• Base of one of the triangles, s = 14 cm

,

• Height of one of the triangles, a = 12.1 cm

First, calculate the area of the hexagonal base.

`\begin{gathered} \text{Area of the hexagonal base}=6*\text{Area of one equilateral triangle} \\ =6*(1)/(2)sa \\ =3*14*12.1 \\ =508.2\; cm^2 \end{gathered}`

Next, calculate the lateral surface area (area of the sides).

The side of the solid is made up of 6 rectangles with dimensions 7cm by 14cm.

`\text{Lateral Surface Area}=6*7*14=588\; cm^2`

Therefore, the surface area of the solid will be:

`\begin{gathered} \text{Total Surface Area=Area of the Top+Area of the base+Lateral Area} \\ =508.2+508.2+588 \\ =1604.4\; cm^2 \end{gathered}`

The total surface area is 1604.4 sq. cm.