Question

An art museum has a pentagon-shaped room. When drawn to scale on a coordinate grid the corners of the room are points A(14, 18) B(10, 18) C(10, 9) D(12, 5) E(14, 5) feet. The walls are 10 feet high. The museum is going to paint four of the walls: one gallon of paint is enough to cover 268 square feet. How many gallons of paint should the museum purchase? Enter your answer as a whole number.

a) 4 gallons
b) 5 gallons
c) 6 gallons
d) 7 gallons

Answer 1

To find the area of the pentagon-shaped room, divide it into three triangles.
Calculate the area of each triangle using the formula for the area of a triangle.
Multiply the total area by 10 and divide by 268 to determine the number of gallons of paint needed, rounding up.

Step-by-step explanation:

To find the area of the pentagon-shaped room, we can divide it into three triangles. Using the formula for the area of a triangle, A = (1/2) * base * height, we can calculate the area of each triangle:

Triangle 1: ABM

Base = 4 units (10 - 14)

Height = 13 units (18 - 5)

Area = (1/2) * 4 * 13 = 26 square units

Triangle 2: BCM

Base = 1 unit (10 - 10)

Height = 9 units (18 - 9)

Area = (1/2) * 1 * 9 = 4.5 square units

Triangle 3: CDE

Base = 2 units (12 - 10)

Height = 0 units (5 - 5)

Area = (1/2) * 2 * 0 = 0 square units

Therefore, the total area of the pentagon-shaped room is 26 + 4.5 + 0 = 30.5 square units.

Now, since the walls are 10 feet high, we need to multiply the total area by 10 to get the total square footage of the walls. 30.5 * 10 = 305 square feet. Since one gallon of paint covers 268 square feet, the museum should purchase 2 gallons of paint (305 / 268 = 1.14). However, since the question asks for the answer as a whole number, the museum should purchase 3 gallons of paint.