Ben made a model (shown below) of the square pyramid he plans to build when he grows up.
Find the surface area of the model.
\text{ m}^2 m
2
start text, space, m, end text, squared

Step-by-step explanation:

The surface area of a square pyramid is the sum of the area of the squared base + 4 times the area of each triangular face, therefore:

where:

is the area of the base, where

L is the length of the base

is the area of each triangular face, where

h is the height of the face

Substituting,

For the model in this problem,

L = 12

h = 8

Therefore, the surface area here is:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.