Question

What is the surface area formula for a rectangular pyramid?

Answer 1

Hint: Now we know that rectangular pyramid is nothing but the pyramid with the base as a rectangle. Hence we will check the properties and the formula to find the total surface area of the rectangular pyramid.

Complete step by step solution:
Now let us first understand the shape of the rectangular pyramid.
Now we know that a rectangular pyramid is a 3 dimensional object with its base as a rectangle and the top as a pyramid. Now since the base is rectangle from below the shape looks like a rectangle which has equal and parallel opposite sides.
Now the shape has 5 surface areas of which 1 surface is rectangular and 4 surfaces are triangular.
Also we can say that there are 5 vertices in the shape of which four are edges of the rectangle and 1 is on the top.
Now let us draw the shape of a rectangular pyramid.

Now let us calculate the area of the rectangular pyramid.
Now if l is the length of rectangular base, w is the width of rectangular base and h is the height of pyramid then we get the surface area of the rectangular pyramid as $A=lw+l\sqrt{{\left({\displaystyle \frac{w}{2}}\right)}^2+h^2}+w\sqrt{{\left({\displaystyle \frac{l}{2}}\right)}^2+h^2}$

Note: Now note that the volume of the rectangular pyramid is given by the formula ${\displaystyle \frac{lwh}{3}}$ . Now suppose we want to find the formula of area or volume for a square pyramid then we will simply substitute l = w in the formula as length and width of square are equal.