Question

In order to determine how much paint he needs to paint the front of his house, Joe is calculating the area he’ll be painting (the shaded region). The door is 7 feet by 3 ft. The large window is 5 ft by 3 ft. Each small window is 2 ft by 3 ft. Show work

Answer 1

Answer:

I found a matching diagram to the question online:

The area to be painted = 464.5 ft²

Step-by-step explanation:

Total area of the figure = area of the rectangle + area of the triangle.

Area of rectangle = Length × Breadth

Length = 25ft

Breadth = 15ft

Area of rectangle = 25 × 15 = 375 ft²

Note that we will subtract the unshaded regions because he will be painting the shaded regions only.

Area of door = 7 × 3 = 21 ft²

Area of large window = 5 × 3 = 15 ft²

Area to be painted on rectangle = total area - area of door - area of large window

= 375 - 21 - 15 = 339 ft²

Next let us solve for the triangle:

Area of triangle = 1/2 base × height

base = 25 ft

height = 26 - 15 = 11 ft

∴ Area of triangle = 0.5 × 25 × 11 = 137.5 ft²

Remember that we will subtract the area of the unshaded part.

unshaded region = 2 small windows

Areas of two small windows = 2 × ( 2 × 3) = 2 × 6 = 12 ft²

Therefore area of shaded portion of triangle = 137.5 - 12 = 125.5 ft²

Total area to be painted = shaded areas of (rectangle + triangle)

= 339 + 125.5 = 464.5 ft²