A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythagoras' Theorem thank you)

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

where B stands for Base area

and P for Base Parimeter

so

now we need our algebraic skills to figure out s

simplify parentheses:

reduce fraction:

simplify multiplication:

cancel 64 from both sides;

divide both sides by 16:

now we'll use Pythagoras theorem to figure out height

according to the theorem

substitute the value of l and s:

simplify parentheses:

simplify squares:

cancel 16 from both sides:

square root both sides:

recall the formula of a square pyramid

where A stands for Base area (l²)

substitute the value of h and l:

simplify multiplication:

reduce fraction:

hence,

14.29%

step-by-step explanation:

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.