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Find the area of the complex figure.
A 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.
Can you help me solve this problem?
To find the area of this figure, there is two choices
1. cut it into 3 rectangles.
2.find the missing rectangle in the middle......
find the missing area in the middle, 12* 23 = 276
the area of the whole figure 31*69-276=1863m²
I know what to do. So we can divide the shape into three rectangles. There should be square and two rectangles. So for the rectangles we will find the lengths. We know that 31 is the total width of rectangle one and two, 12 is the other length but we need to the total length. So, 31 - 12 = 19. Since we have 19 that is going to be the width of our square. We have 23 as our length of the square 19 x 23 = 437. Then. we have 69 as the base of our shape. We can subtract 23 from 69, leaving us with 46. The equation to the area is 46 x 31 + 19 x 23, leaving us with an area of 1863, which is the area.
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Sure! To find the area of the complex figure, we need to break it down into simpler shapes and calculate their individual areas.
First, let's identify all the individual shapes formed by the sides of the figure.
1. Rectangle A: The left-most vertical side, the lower-most horizontal side, and the middle horizontal side form a rectangle.
2. Rectangle B: The middle horizontal side, the upper-right horizontal side, and the upper-middle left vertical side form another rectangle.
3. Square: The upper-right horizontal side, the upper-middle left vertical side, and the right-most vertical side form a square.
Now, we can calculate the areas of each shape separately.
1. Rectangle A:
Length = 31 meters (left-most vertical side)
Width = 69 meters (lower-most horizontal side)
Area of Rectangle A = Length x Width = 31 meters x 69 meters = 2139 square meters
2. Rectangle B:
Length = 23 meters (middle horizontal side)
Width = 12 meters (upper-middle left vertical side)
Area of Rectangle B = Length x Width = 23 meters x 12 meters = 276 square meters
3. Square:
Side length = 23 meters (upper-right horizontal side and upper-middle left vertical side)
Area of Square = Side length x Side length = 23 meters x 23 meters = 529 square meters
Finally, to get the area of the complex figure, we need to add the areas of all the individual shapes together.
Area of Complex Figure = Area of Rectangle A + Area of Rectangle B + Area of Square
= 2139 square meters + 276 square meters + 529 square meters
= 2944 square meters
Therefore, the area of the complex figure is 2944 square meters.