Answer:
\(\text{Total surface area of a paperweight}=64\text{ cm}^2\)
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.
\(\text{Total surface area of a pyramid}=\frac{1}{2}p*l+B\), 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,
\(\text{Total surface area of a paperweight}=\frac{1}{2}*16\text{ cm}*\text{6 cm}+16\text{ cm}^2\)
\(\text{Total surface area of a paperweight}=8\text{ cm}*\text{6 cm}+16\text{ cm}^2\)
\(\text{Total surface area of a paperweight}=48\text{ cm}^2+16\text{ cm}^2\)
\(\text{Total surface area of a paperweight}=64\text{ cm}^2\)
Therefore, total surface area of our given paperweight is 64 square cm.
