Question

Find the surface area of the prism or regular pyramid:

Answer 1

Hint: The prism is composed of 2 triangles and 3 rectangles

Step 1: Surface area of the pyramid is the sum of the areas of all its faces, or the sum of its lateral area and base area.

Step 1: Find the area of base rectangle:

$A_{total}=2A_T+A_1+A_2+A_3$

Where $A_T$ is the area of the triangles & $A_1,A_2,A_3$ are the area of the rectangles.

Now, $A_T=\frac{1}{2}b·h$

Where $b$ is the base of the triangle & $h$ is the height of the triangle.

Now, $b=8\&h=15$

Substituting all these values in the formula,

Area of the triangle:

$$\begin{gathered} A_T=\frac{1}{2}\left(8\right)\left(15\right) \\ {A}_T=60 \end{gathered}$$

Remember There are two similar triangles in the prism.

So, $2A_T=120$

$A_1=l\times w$

Where $l$ is the length & $w$ is the width of the rectangle.

Here, $l=8\&w=7$, putting all the values in the formula

$$\begin{gathered} A_1=8\times 7 \\ {A}_1=56 \end{gathered}$$

Step 2: Area of the vertical leg which is rectangular in shape

$A_2=l\times w$

Where $l$ is the length & $w$ is the width of the rectangle.

Here, $l=15\&w=7$, putting all the values in the formula

$$\begin{gathered} A_2=15\times 7 \\ {A}_2=105 \end{gathered}$$

Step 3: Area of the diagonal leg which is rectangular in shape.

$A_3=l\times w$

Where $l$ is the length & $w$ is the width of the rectangle.

Here, $l=17\&w=7$, putting all the values in the formula

$$\begin{gathered} A_3=17\times 7 \\ {A}_3=119 \end{gathered}$$

Step 4: Total area.

$A_{total}=2A_T+A_1+A_2+A_3$

$$\begin{gathered} A_{total}=120+56+105+119 \\ {A}_{total}=400 \end{gathered}$$

Hence,The total surface area of the regular pyramid in $400c{m}^2$.