a painting is made od 3 concentric squares. the side lenght of the largest square is 24 cm what is the area of the painting
since the three squares are nested, the area of the painting is the area of the largest square: 242
To find the area of the painting, we need to calculate the area of each square and add them together.
The side length of the largest square is given as 24 cm.
The area of a square is calculated by multiplying the side length by itself. So, the area of the largest square (A1) is:
A1 = 24 cm * 24 cm = 576 cm^2.
The middle square would have a side length that is smaller than that of the largest square. Let's call the side length of the middle square "x" cm.
We can find "x" by subtracting twice the width of the square from the side length of the largest square.
x = 24 cm - 2 * width of the square.
Since it is mentioned that the squares are concentric, we can calculate the width of the square by dividing the difference between the side lengths of the largest and smallest squares by 2.
width of the square = (24 cm - side length of the inner square) / 2.
However, the side length of the inner square is not given, so we cannot determine the width of the middle square accurately.
Without the information about the side length of the inner square, we cannot calculate the areas of the other squares or the area of the painting accurately.
To find the area of the painting, you need to calculate the area of each square separately and then subtract the areas of the smaller squares from the larger one.
First, find the area of the largest square by multiplying the length of its side by itself:
Area of the largest square = side length * side length = 24 cm * 24 cm = 576 cm²
Next, calculate the area of the next smaller square. Since the next smaller square is concentric to the largest square, its side length will be 2 cm less on each side. Therefore, the side length of the second square is 24 cm - 2 cm - 2 cm = 20 cm.
Area of the second square = side length * side length = 20 cm * 20 cm = 400 cm²
Finally, find the area of the smallest square. Similarly, its side length will be 2 cm less on each side compared to the second square. So, the side length of the smallest square is 20 cm - 2 cm - 2 cm = 16 cm.
Area of the smallest square = side length * side length = 16 cm * 16 cm = 256 cm²
To find the area of the painting, subtract the areas of the smaller squares from the area of the largest square:
Area of the painting = Area of the largest square - (Area of the second square + Area of the smallest square)
Area of the painting = 576 cm² - (400 cm² + 256 cm²)
Area of the painting = 576 cm² - 656 cm²
Area of the painting = -80 cm²
Therefore, the area of the painting is -80 cm².