Answer:
[tex]\text{Total surface area of a paperweight}=64\text{ cm}^2[/tex]
Step-by-step 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.
[tex]\text{Total surface area of a pyramid}=\frac{1}{2}p*l+B[/tex], where,
[tex]p=\text{Perimeter of the base}[/tex],
[tex]l=\text{Slant height}[/tex],
[tex]B=\text{Area of the base}[/tex].
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.
[tex]\text{Area of the base}=\text{4 cm*4 cm}=16 \text{ cm}^2[/tex]
Upon substituting our given values in total surface area of pyramid we will get,
[tex]\text{Total surface area of a paperweight}=\frac{1}{2}*16\text{ cm}*\text{6 cm}+16\text{ cm}^2[/tex]
[tex]\text{Total surface area of a paperweight}=8\text{ cm}*\text{6 cm}+16\text{ cm}^2[/tex]
[tex]\text{Total surface area of a paperweight}=48\text{ cm}^2+16\text{ cm}^2[/tex]
[tex]\text{Total surface area of a paperweight}=64\text{ cm}^2[/tex]
Therefore, total surface area of our given paperweight is 64 square cm.
