We know that the lateral area of a regular pyramid is half the product of the perimeter p of the base and the slant height l of the pyramid.
L.A.=1/2pl
Although we are not given the slant height of our pyramid, we can find it by using the Pythagorean Theorem. Note that the base of our triangle will be 4 ÷ 2 = 2 meters.
In this right triangle, the legs are 6 and 2 meters long. The hypotenuse is l. We will substitute these values into the Pythagorean Theorem and solve for l.
The hypotenuse of the right triangle, and therefore the slant height of the pyramid, is 2sqrt(10) meters long.
The base of the pyramid is a square with the side length of 4m. Let's calculate its perimeter!
p=4s ⇒ p=4( 4)=16m
With this information, we are now able to calculate the lateral area of the pyramid. We will substitute p=16 and l=2sqrt(10) into the formula for lateral area. Let's do it!
