An art museum has a pentagon-shaped room. when drawn to scale on a coordinate grid, the corners of the room are points (18,20):
b(4,20): c(4,4): d(16.2): e(22.10), shown in feet. the walls are 10 feet high.
the museum is going to paint four of the walls: ab, bc, de, and ae. assume one gallon of paint is enough to cover 400 square feet.
how many gallons of paint should the museum purchase? enter your answer as a whole number.

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

we have

step 1

Find the distance AB

we have

substitute in the formula

step 2

Find the distance BC

we have

substitute in the formula

step 3

Find the distance DE

we have

substitute in the formula

step 4

Find the distance AE

we have

substitute in the formula

step 5

Find out the area of the four walls

To determine the area sum the length sides and multiply by the height of the walls

so

substitute the given values

The height of the walls is 10 ft

step 6

Determine the number of gallons needed to paint the four walls

we know that

one gallon of paint is enough to cover 400 square feet

using proportion

Round up

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2