Company wants to paint its logo on the side of a building. The entire area needs to be covered with a primer. The two triangular areas will be painted red. The rectangle containing the company’s name will be white, and the rest of the parallelogram will be yellow.
a. Find the area for each different color
b. Find the area that must be painted with primer
The Correct Answer and Explanation is:
To provide an accurate answer, I need to know the dimensions of the shapes involved (triangles, rectangle, and parallelogram). Since the problem doesn’t give specific numbers, I will explain using variables and an example. Let’s assume the following scenario:
Assumed Dimensions
- Parallelogram (entire shape): Base = 20 m, Height = 10 m
- Each Triangle (2 total): Base = 5 m, Height = 4 m
- Rectangle (company name): Length = 10 m, Height = 2 m
a. Find the area for each different color
- Red (2 Triangles)
Area of one triangle = ½ × base × height = ½ × 5 × 4 = 10 m²
Total red area = 2 × 10 = 20 m² - White (Rectangle)
Area = length × height = 10 × 2 = 20 m² - Yellow (Remaining area of parallelogram)
Total area of parallelogram = base × height = 20 × 10 = 200 m²
Yellow area = Total area − Red area − White area
Yellow area = 200 − 20 − 20 = 160 m²
b. Find the area that must be painted with primer
The entire parallelogram (including all colored regions) needs to be primed first:
Primer area = 200 m²
Explanation
In this painting project, the company wants its logo to be displayed on a large wall shaped like a parallelogram. The entire surface must first be covered with a primer to ensure the paint adheres properly and to provide a consistent base color. After priming, specific regions of the wall will be painted in different colors: red for two triangular areas, white for the rectangular area containing the company name, and yellow for the remaining background.
To solve this, we calculate the area of each individual shape using geometry formulas:
- The parallelogram’s area is found using the formula base × height. This gives us the total wall area.
- Each triangle’s area is found using ½ × base × height. Since there are two identical triangles, we double this result.
- The rectangle is calculated with length × height.
Once we have all the colored region areas, we subtract the red and white parts from the total area to find the yellow region. Importantly, since every part of the wall is eventually painted, all of it must first be primed. Therefore, the primer area is equal to the total area of the parallelogram.
Understanding area calculations in this context is crucial for planning resources, such as how much primer and each paint color is needed, which directly affects budgeting and scheduling in real-world projects.
