Question

A net of a square pyramid is shown below.

What is the surface area, in square centimeters, of the pyramid?

Answer 1

Option (B) 86.7 is the correct answer.

Step-by-step Step-by-step explanation :

Dividing the given diagram in 5 parts :

Firstly finding the area of one right angle triangle :

`\dashrightarrow\sf{Area_((\triangle)) = (1)/(2) * b * h}`

• ↠ b (base) = 5.1 cm
• ↠ h (height) = 5.95 cm

substituting all the given values in the formula :

`\dashrightarrow\sf{Area_((\triangle)) = (1)/(2) * 5.1 * 5.95}`

`\dashrightarrow\sf{Area_((\triangle)) = (1 * 5.1 * 5.95)/(2)}`

`\dashrightarrow\sf{Area_((\triangle)) = (5.1 * 5.95)/(2)}`

`\dashrightarrow\sf{Area_((\triangle)) = (30.345)/(2)}`

`\dashrightarrow\sf{Area_((\triangle)) = 15.1725\: {cm}^(2)}`

Hence, the area of right angle triangle is 15.1725 cm².

`\begin{gathered} \end{gathered}`

Here we have 4 right angle triangle with equal base and height and we have already find the area of one right angle triangle. So, the area of 4 triangle will be :

`\dashrightarrow\sf{Area_((\triangle)) = 15.1725 \: {cm}^(2)}`

`\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 15.1725 * 4}`

`\dashrightarrow\sf{Area \: of \: 4{(\triangle)} = 60.69 \: {cm}^(2)}`

Hence, the area of 4 right angle triangles is 60.69 cm².

`\begin{gathered} \end{gathered}`

Now, we have to find the area of square

`\longrightarrow\sf{Area_((Square)) = {a}^(2)}`

• ↠ a (side) = 5.1 cm

Substituting the given value in the formula :

`\longrightarrow\sf{Area_((Square)) = {(5.1)}^(2)}`

`\longrightarrow\sf{Area_((Square)) = {(5.1 * 5.1)}}`

`\longrightarrow\sf{Area_((Square)) = 26.01 \: {cm}^(2)}`

Hence, the area of square is 26.01 cm².

`\begin{gathered} \end{gathered}`

Now, calculating the total area :

`{\sf{\implies{Total \: Area = Area_((\triangle)) + Area_((Square))}}}`

• ↠ Area of triangle = 60.69 cm²
• ↠ Area of square = 26.01 cm².

`{\sf{\implies{Total \: Area = 60.69 + 26.01}}}`

`{\sf{\implies{Total \: Area = 86.7 \: {cm}^(2)}}}`

Hence, the total area of given diagram is 86.7 cm².

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