If x = 6 units, y = 6 units, and h = 8 units, find the area of the trapezoid shown above using decomposition.
5 answers
We do not have a drawing or an image of the trapezoid shown above. Therefore, we cannot solve the problem. Please provide the relevant information.
middle of trapezoid has h in the middle and y at the bottom right and left sides are cut off. right side has x on top left also has x on top
To use decomposition, we need to split the trapezoid into two smaller shapes, a rectangle and a right triangle.
First, let's find the height of the triangle. Since the midpoint of the trapezoid has height h and the bottom base has length y, each half of the triangle has a height of h/2 and a base of y/2. Therefore, the area of the triangle is:
(1/2)(y/2)(h/2) + (1/2)(y/2)(h/2) = (1/4)(y)(h)
Next, we need to find the area of the rectangle that makes up the bottom half of the trapezoid. The base of the rectangle is the length of the bottom of the trapezoid, which is y. The height of the rectangle is the difference in height between the bottom of the trapezoid (which is 0) and the midpoint of the trapezoid (which is h). Therefore, the area of the rectangle is:
y*h
Adding the area of the triangle and the area of the rectangle gives us the total area of the trapezoid:
(1/4)(y)(h) + y*h = (5/4)(y)(h)
Now, we just need to plug in the given values:
(5/4)(6)(8) = 30 square units
Therefore, the area of the trapezoid is 30 square units.
First, let's find the height of the triangle. Since the midpoint of the trapezoid has height h and the bottom base has length y, each half of the triangle has a height of h/2 and a base of y/2. Therefore, the area of the triangle is:
(1/2)(y/2)(h/2) + (1/2)(y/2)(h/2) = (1/4)(y)(h)
Next, we need to find the area of the rectangle that makes up the bottom half of the trapezoid. The base of the rectangle is the length of the bottom of the trapezoid, which is y. The height of the rectangle is the difference in height between the bottom of the trapezoid (which is 0) and the midpoint of the trapezoid (which is h). Therefore, the area of the rectangle is:
y*h
Adding the area of the triangle and the area of the rectangle gives us the total area of the trapezoid:
(1/4)(y)(h) + y*h = (5/4)(y)(h)
Now, we just need to plug in the given values:
(5/4)(6)(8) = 30 square units
Therefore, the area of the trapezoid is 30 square units.
also forgot to say x=6, y=6, and h=8
Using the values x=6, y=6, and h=8, we can follow the same process as above.
Let's find the height of the triangle first. Each half of the triangle has a height of h/2 = 4 units and a base of x = 6 units. Therefore, the area of the triangle is:
(1/2)(6)(4) + (1/2)(6)(4) = 12 square units
Next, let's find the area of the rectangle that makes up the bottom half of the trapezoid. The base of the rectangle is the length of the bottom of the trapezoid, which is y = 6 units. The height of the rectangle is the difference in height between the bottom of the trapezoid (which is 0) and the midpoint of the trapezoid (which is h = 8 units). Therefore, the area of the rectangle is:
6*8 = 48 square units
Adding the area of the triangle and the area of the rectangle gives us the total area of the trapezoid:
12 + 48 = 60 square units
Therefore, the area of the trapezoid is 60 square units.
Let's find the height of the triangle first. Each half of the triangle has a height of h/2 = 4 units and a base of x = 6 units. Therefore, the area of the triangle is:
(1/2)(6)(4) + (1/2)(6)(4) = 12 square units
Next, let's find the area of the rectangle that makes up the bottom half of the trapezoid. The base of the rectangle is the length of the bottom of the trapezoid, which is y = 6 units. The height of the rectangle is the difference in height between the bottom of the trapezoid (which is 0) and the midpoint of the trapezoid (which is h = 8 units). Therefore, the area of the rectangle is:
6*8 = 48 square units
Adding the area of the triangle and the area of the rectangle gives us the total area of the trapezoid:
12 + 48 = 60 square units
Therefore, the area of the trapezoid is 60 square units.