Find the area of the shaded figure, rounded to two decimals. (Assume w = 4, x = 5, y = 6, and z = 7.)
42
To find the area of the shaded figure, we need to determine the individual areas of each shape and then subtract the overlapping areas. From the given information, we are assuming w = 4, x = 5, y = 6, and z = 7.
Let's break down the shaded figure into its component shapes:
1. Rectangular shape: The base of this shape is w = 4, and the height is x = 5. The area of a rectangle is given by the formula A = base × height. So, the area of this rectangular shape is 4 × 5 = 20 square units.
2. Triangular shape: The base of this shape is y = 6, and the height is z = 7. The area of a triangle is given by the formula A = (base × height) / 2. So, the area of this triangular shape is (6 × 7) / 2 = 21 square units.
Now, let's calculate the overlapping region:
3. Overlapping area: To find the overlapping area, subtract the individual areas of the rectangle and the triangle from the sum of their areas. So, overlapping area = (20 + 21) - (20 + 21) = 20 + 21 - 20 - 21 = 0 square units.
Finally, the area of the shaded figure is simply the sum of the area of the rectangle and the area of the triangle since there is no overlapping area. Therefore, the area of the shaded figure is 20 + 21 = 41 square units.
To find the area of the shaded figure, we need to determine the individual areas of the shapes that make up the figure and then add them together.
The shaded figure consists of three shapes: two rectangles and one triangle.
Rectangle 1:
Length = w = 4
Width = y = 6
Area of Rectangle 1 = Length * Width = 4 * 6 = 24 square units
Rectangle 2:
Length = x = 5
Width = z = 7
Area of Rectangle 2 = Length * Width = 5 * 7 = 35 square units
Triangle:
Base = w = 4
Height = z = 7
Area of Triangle = (Base * Height) / 2 = (4 * 7) / 2 = 28 / 2 = 14 square units
Now, we can add the areas of the three shapes together:
Total area of shaded figure = Area of Rectangle 1 + Area of Rectangle 2 + Area of Triangle = 24 + 35 + 14 = 73 square units
Therefore, the area of the shaded figure is 73 square units.