It x = 4 units, y = B units, and h = 7 units, find the area of the parallelogram shown above using decomposition
To find the area of the parallelogram, we can decompose it into two right triangles and one rectangle.
The total area of the parallelogram will be the sum of the areas of the two right triangles and the rectangle.
The area of the rectangle is given by the formula: Area = base x height. In this case, the base is x = 4 units and the height is h = 7 units. Therefore, the area of the rectangle is 4 x 7 = 28 square units.
Next, we need to find the area of the two right triangles. The area of a triangle is given by the formula: 1/2 x base x height.
For the first right triangle, the base is x = 4 units and the height is y = B units. Therefore, the area of the first triangle is 1/2 x 4 x B = 2B square units.
For the second right triangle, the base is also x = 4 units and the height is h = 7 units. Therefore, the area of the second triangle is 1/2 x 4 x 7 = 14 square units.
Adding up the areas of all three shapes, we get:
Area = Rectangle + Triangle 1 + Triangle 2
Area = 28 + 2B + 14
Area = 42 + 2B square units
Therefore, the area of the parallelogram is 42 + 2B square units.