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

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

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step-by-step explanation: