Answers:
Area = 78 cm^2
Perimeter = 42 cm
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Step-by-step explanation:
Refer to the diagram below.
I've added points and labels, along with the dashed lines to break up the figure into three rectangles. The points in blue are the corner points of the original figure. The red points help set up the dashed lines.
Along the very top, we have BC = 8 cm, which breaks down into BK = 6 and KC = 2. Opposite of side KC is GJ = 2. For any rectangle, the opposite sides are always the same length.
Side AB = 9 cm. The three vertical sides of CD, EF, and GH all must add to get 9 cm in total, since the right side is the same height as the left side. We are given that EF = 3 and GH = 3, which must mean CD = 3 as well.
Through similar logic, the sides BC = 8 and DE = 4 add to 8+4 = 12 cm total. This total distance across the top must match the total distance along the bottom; i.e. the bottom horizontal sides of AH and GF must add to 12 as well. We are given AH = 6, so GF = 6 also.
Recall earlier we found GJ = 2. If GF = 6, then that leads to JF = 4.
In other words, GJ+JF = 2+4 = 6 = GF.
All of this is visually shown in the diagram shown below.
Once you have the diagram set up as shown, it's fairly straight forward from here. Compute the area of each of the three smaller rectangles and then add up those smaller areas to get the overall area.
I'll work from left to right to find the areas:
- Rectangle ABKH has area of 9*6 = 54 cm^2
- Rectangle GKCJ has area 6*2 = 12 cm^2
- Rectangle JDEF has area 3*4 = 12 cm^2
The total area of the composite figure is therefore: 54+12+12 = 78 cm^2
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The perimeter is the sum of all the external sides. We'll ignore the dashed lines as they are not exterior segments.
perimeter = sum of exterior sides
perimeter = AB+BC+CD+DE+EF+FG+GH+HA
perimeter = 9+8+3+4+3+6+3+6
perimeter = 42 cm
Notes:
- To keep things organized, I'm working clockwise when going from AB to BC to CD etc
- There are a total of 8 exterior sides being added up to get the perimeter.