why the formula for the area of a trapezoid this A=1/2 x h x(a+b)
The formula for the area of a trapezoid is A = 1/2 * h * (a + b), where "A" represents the area, "h" represents the height, and "a" and "b" represent the lengths of the parallel sides of the trapezoid.
To understand why this formula is used, let's break it down step by step:
1. The first step is multiplying the height by the sum of the lengths of the parallel sides. This is represented by (a + b). This multiplication gives us the sum of the areas of the two equal-sized triangles that make up the top and bottom sections of the trapezoid.
2. Next, we multiply the obtained sum by 1/2. Since the triangles have equal areas, we divide the sum by 2 to find the area of a single triangle.
Combining steps 1 and 2, we end up with the formula A = 1/2 * h * (a + b), which calculates the area of the trapezoid.
In summary, the formula takes the sum of the areas of two triangles within the trapezoid and divides it by 2 to calculate the total area.
draw any trapezoid
draw a diagonal
isn't the height between the two parallel sides constant? Let it be h
let the two parallel sides be a and b
so now you have two triangles where you know the height, h, and the sides
first triangle area = (1/2)ah
2nd triangle area = (1/2)bh
total = (1/2)ah + (1/2)hb
common factor of (1/2)h
gives us
(1/2)h(a+b)