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

im here

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.