Problem 2
Check out the attached image below. I've subdivided the figure into various rectangles and triangles. The reason for this is because we'll then use the area formulas for rectangles and triangles. After finding the area of each little sub-region, you add them up to get the final answer.
We have these six regions: A, B, C, D, E, F
Regions B and D are squares, while everything else is a triangle
- area of region A = base*height/2 = 1*3/2 = 1.5
- area of region B = base*height = 1*1 = 1
- area of region C = base*height/2 = 1*2/2 = 1
- area of region D = base*height = 1*1 = 1
- area of region E = base*height/2 = 1*2/2 = 1
- area of region F = base*height/2 = 1*3/2 = 1.5
Add up those results:
1.5+1+1+1+1+1.5 = 7
Answer: 7 square units
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Problem 4
The figure is divided into various smaller pieces similar to the previous problem. There are probably a few different ways to subdivide.
This time nearly everything is a triangle, with the lone exception being region D which is a rectangle.
- region A = base*height/2 = 1*2/2 = 1
- region B = base*height/2 = 1*2/2 = 1
- region C = base*height/2 = 2*1/2 = 1
- region D = base*height = 2*1 = 2
- region E = base*height/2 =1*1/2 = 0.5
- region F = base*height/2 = 3*1/2 = 1.5
- region G = base*height/2 =1*1/2 = 0.5
Add up the subtotals
A+B+C+E+F+G = 1+1+1+2+0.5+1.5+0.5 = 7.5
Answer: 7.5 square units
