The lateral surface area of a regular pyramid is 160 cm2 and the perimeter of the base is 40 cm. What is the slant height?
I forgot to put the possible answers,
a.) 4cm
b.) 8cm
c.) 10cm
See repost:
http://www.jiskha.com/display.cgi?id=1275672571
thanks :)
To find the slant height of a regular pyramid, we can use the lateral surface area and the perimeter of the base.
First, let's understand the lateral surface area of a regular pyramid. The lateral surface area is the sum of the areas of all the triangular faces excluding the base.
In this case, the lateral surface area is given as 160 cm². This means that the sum of the areas of all the triangular faces is 160 cm².
Now, let's find the area of one triangular face. Since the pyramid is regular, all the triangular faces are congruent (i.e., their dimensions and shape are the same).
Since the perimeter of the base is given as 40 cm, and the base of the pyramid is a polygon with equal sides, we can find the length of each side of the base by dividing the perimeter by the number of sides.
In this case, the base has 40 cm as its perimeter, and since it's a regular pyramid, it must be a square. Therefore, each side length of the base is 40 cm divided by 4, which equals 10 cm.
Now that we have the side length of the base, we can calculate the area of one triangular face. Since the base is a square, the height of the triangular face is the slant height of the pyramid. Thus, the area of the triangular face is (1/2) * base * height.
Substituting the values, we get:
Area of one triangular face = (1/2) * 10 cm * height = 5 cm * height
Since the lateral surface area is the sum of the areas of all the triangular faces and is given as 160 cm², we can set up the equation:
160 cm² = 5 cm * height * number of faces
A regular pyramid with n faces has n-1 triangular faces, so in this case, the number of faces is 4. Substituting this into the equation:
160 cm² = 5 cm * height * 4
Simplifying the equation:
160 cm² = 20 cm * height
To solve for the height, we can divide both sides of the equation by 20 cm:
160 cm² / 20 cm = height
height = 8 cm
Therefore, the slant height of the regular pyramid is 8 cm.