Answer: 25 s^2 (units squared)
Explanation:
What we know:
- This figure is arranged on a grid
- We can split the figure into basic shapes
- The formula for the area of a triangle is A = (1/2)bh
- The formula for the area of a right triangle is A = (1/2)ab
How to solve:
By splitting this shape into a few triangles, we can combine their areas to find the total area of the more complex shape.
These will be one right triangle, represented by the formula A = (1/2)ab, where both a and b variables are one of the legs of the triangle. And, these will be two triangles, represented by the formula A = (1/2)bh, where b is the base and h is the height.
Their areas will be represented in s^2, squares squared.
Process:
Triangle 1 (A = (1/2)ab)
Set up equation A = (1/2)ab
Substitute A = (1/2)(2)(4)
Simplify A = (1/2)(8)
Simplify A = 4 s^s
Triangles 2 & 3 (A = (1/2)bh)
Set up equation A = (1/2)bh
Substitute A = (1/2)(6)(4)
Simplify A = (1/2)(24)
Simplify A = 12 s^2
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Set up equation A = (1/2)bh
Substitute A = (1/2)(6)(3)
Simplify A = (1/2)(18)
Simplify A = 9 s^2
Total Area
Where A is the total area, x is the area of the first triangle, y is the area of the second triangle, and z is the area of the third triangle.
Set up equation A = x+y+z
Substitute A = 4 + 12 +9
Simplify A = 16 + 9
Simplify A = 25 s^2
Answer: 25 s^2 (units squared)
