The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find:
Lateral area of the pyramid
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find: Lateral area of the pyramid
Explain again plz
quadrilateral. four sides
regular: all sides are the same
you have one face, what now is four faces?
Have I missed something?
To find the lateral area of the pyramid, we need to determine the perimeter of the base. However, since a regular quadrilateral pyramid has a square base, we can find the perimeter by using the formula for the perimeter of a square.
The area of the base is given as 36 cm^2. Since the base is a square, we can find the length of one side by taking the square root of the area:
Side length = √36 = 6 cm.
Now that we know the side length, we can calculate the perimeter by multiplying it by 4:
Perimeter of the base = 4 * 6 = 24 cm.
Since each lateral face of the pyramid is a triangle, we can use the formula for the area of a triangle to find the lateral area. The area of a triangle is given by the formula:
Area of a triangle = (base * height) / 2.
The base of the lateral face is equal to the perimeter of the base (24 cm), and the height is the slant height of the pyramid (which is the height of the lateral face). Since the pyramid is regular, the slant height is the same as the height of the lateral face.
So, the area of a lateral face is 48 cm^2. Plugging in the values, we get:
48 = (24 * height) / 2.
We can solve for the height using algebra:
48 = 12 * height,
height = 48 / 12 = 4 cm.
Now that we have the height, we can calculate the lateral area of the pyramid by multiplying the perimeter of the base by the height of the lateral face:
Lateral area of the pyramid = Perimeter of the base * Height of the lateral face,
Lateral area of the pyramid = 24 cm * 4 cm = 96 cm^2.
Therefore, the lateral area of the pyramid is 96 cm^2.