CPM Homework Help : GC Problem 11-100

On your paper, draw a diagram of a square-based right pyramid. If the base has side length $6$ units and the height of the pyramid is $10$ units, find the total surface area. Show all your work.

Hint:

Use the Pythagorean Theorem to find the slant height of the pyramid, which will be referred to as x.

More Help:

$10^2 + 3^2 = x^2$

$x = \sqrt{109}$

Square pyramid, with dashed right triangle. Vertical leg, labeled, 10, from top vertex, to center of base, Horizontal leg, labeled, 3, from center, to middle point on right edge of base, Hypotenuse, labeled, x, from vertex, to middle point on right edge of base.

Hint 2:

Now that you know the slant height you can find the area of the four triangles that make up the pyramid.
Afterwards, add the area of the four triangles to the area of the pyramid's base in order to find the total surface area of the pyramid.

Answer:

$161.28\text{ units}^2$