A pyramid has a volume of 1,944 inches cubed and a rectangular base with the dimensions 18 inches by 9 inches. What is the heigh
2 answers:
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Answer:
The length of the slant height of the square pyramid is 20 in.
Step-by-step explanation:
The lateral surface area of a regular pyramid is the sum of the areas of its lateral faces.
The general formula for the lateral surface area of a regular pyramid is
where represents the perimeter of the base and
the slant height.
From the information given we know that:
- The lateral surface area of a square pyramid is 440 in².
- The area of the base is 121 in².
And we want to find the the slant height of the pyramid.
For this, we also need to know that the area of a square is given by , where <em>s</em> is the length of any side and the perimeter of a square is given by
.
Applying the formula for the area of a square we can find the length of the side
The perimeter of the base is
Next, we can apply the formula for the lateral surface area and solve for the slant height.
The length of the slant height of the square pyramid is 20 in.