Question

Find the surface area of the regular pyramid.

Answer 1

Hint: Identify the type of pyramid & remember the formula of the surface area of the regular pyramid.

The surface area $S$ of a pyramid is the sum of the areas of the base and the lateral faces.

$S=areaofbase+areasoflateralfaces$

Now, This pyramid is having triangle base and the lateral faces are triangles.

Step 2: Area of triangular base,

$B=\frac{1}{2}\times w\times l$

Where $w$ is the width and $l$ is the length of the triangular cross-section.

Area of lateral face,

$B=\frac{1}{2}\times w\times l$

Where $w$ is the width and $l$ is the length of the triangular cross-section.

Step 3: Area of the triangular base,

$B=\frac{1}{2}\times w\times l$

Width $w$ is 7 centimeters & length $l$ is 6 centimeters.

$$\begin{gathered} A=\frac{1}{2}\left(6\right)\left(7\right) \\ =21 \end{gathered}$$

Let’s substitute the values in the formula,

Width $w$ of the lateral face is 7 centimeters & length $l$ of the lateral face is 9 centimeters.

$$\begin{gathered} B=\frac{1}{2}\times w\times l \\ B=\frac{1}{2}\left(7\right)\left(9\right) \\ =31.5 \end{gathered}$$

$$\begin{gathered} S=areaofbase+areasoflateralfaces \\ S=21+3(31.5) \end{gathered}$$

As there are 3 lateral faces in the given figure,

$$\begin{gathered} S=21+94.2 \\ S=115.5 \end{gathered}$$

Final answer: The surface area is 115.5 square centimeters.