If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.
It's not possible to answer this question without a visual or diagram to reference. Please provide additional information.
baseball diamond is a square with corners at home plate, first base, second base, and third base. The distance between home plate and first base is 30 yards. What is the area of a baseball diamond?
Since the baseball diamond is a square, each side has a length of 30 yards (the distance between home plate and first base). Therefore, the area of the square is:
30 yards x 30 yards = 900 square yards
So the area of a baseball diamond is 900 square yards.
If x = 8 units, y = 4 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
It's not possible to answer this question without a visual or diagram to reference. Please provide additional information.
If x = 8 units, y = 4 units, and h = 4 units
Assuming that the rhombus is positioned with one corner at the bottom left and the other corner at the top right, we can use the formula for the area of a rhombus:
A = (x * h) / 2
In this case, x = 8 units and h = 4 units. Substituting these values into the formula, we get:
A = (8 * 4) / 2
A = 32 / 2
A = 16 square units
Therefore, the area of the rhombus is 16 square units.
Find the area of the isosceles trapezoid below by using the area formulas for rectangles and triangles.
a = 6 cm, b = 10 cm, and c = 3 cm
In an isosceles trapezoid, the two non-parallel sides (a and c in this case) are equal in length. Therefore, we can draw a perpendicular line from the midpoint of the top side (b in this case) down to the bottom side, creating two right triangles and a rectangle as shown below:
```
________
/ \
/ \
/ \
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```
The height of the trapezoid is the same as the height of the two triangles, which we can find using the Pythagorean theorem:
h = sqrt(a^2 - ((b-c)/2)^2)
h = sqrt(6^2 - ((10-3)/2)^2)
h = sqrt(27.25)
h ≈ 5.22 cm
The area of each triangle is (1/2) * a * h, so the total area of both triangles is:
A_triangles = 2 * (1/2) * a * h
A_triangles = a * h
A_triangles = 6 cm * 5.22 cm
A_triangles ≈ 31.32 cm^2
The area of the rectangle is b * h, so:
A_rectangle = b * h
A_rectangle = 10 cm * 5.22 cm
A_rectangle ≈ 52.2 cm^2
The total area of the trapezoid is the sum of the areas of the triangles and the rectangle:
A_trapezoid = A_triangles + A_rectangle
A_trapezoid ≈ 83.52 cm^2
Therefore, the area of the isosceles trapezoid is approximately 83.52 square centimeters.