Question

paul has a paperweight shaped like a square pyramid shown what is the total area in square centermeters

Answer 1

here is the picture to your problem

Answer 2

`\text{Total surface area of a paperweight}=64\text{ cm}^2`

Explanation:

We have been given a picture of a paperweight which is shaped like a square pyramid. We are asked to find the total surface area of the paperweight.

We will use total surface area formula of a regular pyramid to find the total surface area of our given paperweight.

`\text{Total surface area of a pyramid}=(1)/(2)p*l+B`, where,

`p=\text{Perimeter of the base}`,

`l=\text{Slant height}`,

`B=\text{Area of the base}`.

Since base of our pyramid is square, so perimeter of the base will be 4 times length of each side of square (4*4=16) cm.

`\text{Area of the base}=\text{4 cm*4 cm}=16 \text{ cm}^2`

Upon substituting our given values in total surface area of pyramid we will get,

`\text{Total surface area of a paperweight}=(1)/(2)*16\text{ cm}*\text{6 cm}+16\text{ cm}^2`

`\text{Total surface area of a paperweight}=8\text{ cm}*\text{6 cm}+16\text{ cm}^2`

`\text{Total surface area of a paperweight}=48\text{ cm}^2+16\text{ cm}^2`

`\text{Total surface area of a paperweight}=64\text{ cm}^2`

Therefore, total surface area of our given paperweight is 64 square cm.