Find the area of the complex figure.
The figure has 8 sides, all sides meet at right angles. The left-most vertical side measures 31 meters. The lower most horizontal side measures 69 meters. The right-most vertical side measures 31 meters. The upper right horizontal side measures 23 meters.The middle horizontal side measures 23 meters. The upper middle left vertical side measures 12 meters.
Just divide the figure up into rectangles. You can then see the width and height of each part, and add up all the smaller areas.
To find the area of the complex figure, you can divide it into smaller rectangles and triangles, and then sum up their areas.
Step 1: Divide the figure into rectangles:
- There are two rectangles in this complex figure. One rectangle is formed by the left-most vertical side, the lower-most horizontal side, and the middle horizontal side. The other rectangle is formed by the middle horizontal side, the upper right horizontal side, and the upper middle-left vertical side.
Step 2: Calculate the area of the rectangles:
- The area of a rectangle is given by the formula: length × width.
- For the first rectangle, the length is 31 meters and the width is 69 meters.
- For the second rectangle, the length is 23 meters and the width is 12 meters.
Step 3: Divide the figure into triangles:
- There are two triangles in this complex figure. One triangle is formed by the left-most vertical side, the middle horizontal side, and the upper middle-left vertical side. The other triangle is formed by the upper right horizontal side, the middle horizontal side, and the upper middle-left vertical side.
Step 4: Calculate the area of the triangles:
- The area of a triangle is given by the formula: (base × height) / 2.
- For the first triangle, the base is 31 meters and the height is 12 meters.
- For the second triangle, the base is 23 meters and the height is 12 meters.
Step 5: Sum up the areas:
- Add the areas of the rectangles and the triangles to get the total area of the complex figure.
Let's calculate the area:
Area of first rectangle = 31 meters × 69 meters
Area of second rectangle = 23 meters × 12 meters
Area of first triangle = (31 meters × 12 meters) / 2
Area of second triangle = (23 meters × 12 meters) / 2
Total area = Area of first rectangle + Area of second rectangle + Area of first triangle + Area of second triangle
Now, you can plug in the values and calculate the area.