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The pyramids are similar.
a. Find the missing dimension.
b. Find the surface area of the red pyramid.

$5$ . The pyramids are similar. $\newline$ a. Find the missing dimension. $\newline$ b. Find the surface area of the red pyramid.

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Find the magnitude of a three-dimensional vector

Full solution

Q.

5

. The pyramids are similar.

\newline

a. Find the missing dimension.

\newline

b. Find the surface area of the red pyramid.

Find Scale Factor: a. To find the missing dimension, we need to use the scale factor between the two similar pyramids. $\newline$ Let's say the scale factor is $k$ .
Calculate Proportion: If the height of the smaller pyramid is $h$ and the larger pyramid is $kh$ , then we can write the proportion for the missing dimension.
Calculate Dimensions: Assuming we have the dimensions for the base and height of the smaller pyramid, we can calculate $k$ using the corresponding dimensions of the larger pyramid.
Find Surface Area: b. To find the surface area of the red pyramid, we need to calculate the area of the base and the area of the triangular faces.
Calculate Base Area: The surface area (SA) of a pyramid is given by $SA = \text{Base Area} + \frac{1}{2} \times \text{Perimeter of Base} \times \text{Slant Height}$ .
Calculate Slant Height: Calculate the base area using the base dimensions.
Calculate Total Surface Area: Calculate the slant height using the Pythagorean theorem if necessary.
Calculate Total Surface Area: Calculate the slant height using the Pythagorean theorem if necessary.Add up the base area and the areas of the triangular faces to get the total surface area.

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