Question 1:
Find the area of the triangle (in square units) by decomposition.
To find the area of a triangle by decomposition, we can divide the triangle into simpler shapes whose area we can easily calculate.
Let's consider a triangle with base 8 units and height 5 units.
We can decompose this triangle into two right triangles by drawing a vertical line from the top vertex to the base, creating two right triangles with bases of 4 units each and heights of 5 units.
The area of a triangle is given by the formula: Area = 1/2 * base * height
Area of the first right triangle = 1/2 * 4 * 5 = 10 square units
Area of the second right triangle = 1/2 * 4 * 5 = 10 square units
Therefore, the total area of the triangle is the sum of the areas of the two right triangles: 10 square units + 10 square units = 20 square units.
So, the area of the triangle is 20 square units.