Question

PLEASE HELP WILL GIVE BRAINLIEST AND 20 POINTS

Answer 1

15 inches.

The side length of the base is 4. Find the surface area of the base only by squaring the side length - 4² - which is 16. The surface area of the base is 16 in². 

The surface area of the entire pyramid can be found using this equation:

$SA = B + \frac{1}{2} nbl$ 

Where:
- SA is the surface area (136 square inches)
- B is the area of the base (16 square inches)
- n is the number of triangles (4, because it's a square pyramid)
- b is the base length (4 inches)
- l is the slant length

Note that we have many parts of this equation, and all we need is the slant length. So, let's format the equation with what we have:

$136 = 16 + \frac{1}{2} * 4 * 4 * l$

So then we want to solve for l, the slant height. So, start by subtracting 16 from each side. This would give us: 

$120 = \frac{1}{2} * 4 * 4 * l$

Now, multiply both sides by 2 to get rid of the fraction:

$240 = 4 * 4 * l$

Finally, divide both sides by four, twice (divide by 16):

$15 = l$

So, we know that the slant height of this pyramid is 15 inches.