A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?

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A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?

The height of the trapezoid (or the land) is 4.5 feet.

To find the height of the trapezoid, we need to first find the length of the parallel sides of the trapezoid, which will be the length of the shed.

Given that Jackson wants to put a 4-foot by 4-foot shed on the land, the base of the trapezoid will be 4 feet. Now, we need to find the length of the other parallel side.

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Since the total area of the land is 33.75 square feet and one of the bases of the trapezoid (shed) is 4 feet, we can find the length of the other base (let’s call it x) using the formula for the area of a trapezoid:

A = 1/2 * h * (b1 + b2)

Where:

• A is the area of the trapezoid (which is the total area of the land in this case),
• h is the height of the trapezoid (which we’re trying to find),
• b1 and b2 are the lengths of the parallel sides of the trapezoid (the shed base and the other side’s length).

Given A = 33.75, b1 = 4, and b2 = x, we have:

33.75 = 1/2 * h * (4 + x)

Now, plug in the given condition that the height of the trapezoid must be at least 4.5 feet:

4.5 ≤ h

Now, solve the equation for x:

33.75 = 1/2 * 4.5 * (4 + x) 33.75 = 2.25 * (4 + x) 33.75 = 9 + 2.25x 2.25x = 33.75 – 9 2.25x = 24.75 x = 24.75 / 2.25 x = 11

Now, we have found that the other base of the trapezoid (the length of the land parallel to the shed base) is 11 feet. So, the height of the trapezoid (or the land) is:

h = 4.5 feet

Therefore, the height of the trapezoid (or the land) is 4.5 feet.

Properties of Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. Here are some of its key properties:

1. Parallel sides: A trapezoid has at least one pair of parallel sides. These parallel sides are called the bases of the trapezoid.

2. Non-parallel sides: The non-parallel sides of a trapezoid are called legs or lateral sides.

3. Angles: The angles formed between the non-parallel sides and the bases are called the base angles. In an isosceles trapezoid (where the non-parallel sides are equal in length), the base angles are also equal.

4. Height: The perpendicular distance between the bases of a trapezoid is called its height. The length of the height is typically measured from one base to the other.

5. Median: The median of a trapezoid is the line segment connecting the midpoints of the non-parallel sides. It’s parallel to the bases and its length is the average of the lengths of the bases.

6. Area: The area of a trapezoid can be calculated using the formula: Area = (1/2) × (sum of bases) × height Alternatively, if you know the lengths of both bases and the height, you can use the formula: Area = (1/2) × (b1 + b2) × h where b1 and b2 are the lengths of the bases, and h is the height.

7. Diagonals: A trapezoid has two diagonals. These diagonals are not necessarily equal in length or perpendicular to each other. They divide the trapezoid into four triangles.

8. Symmetry: Trapezoids are not generally symmetric figures, but isosceles trapezoids have an axis of symmetry parallel to their bases, passing through the midpoints of the non-parallel sides.

9. Sum of interior angles: The sum of the interior angles of a trapezoid is always equal to 360 degrees.

Remember, various types of trapezoids may have additional properties or specific relationships between their sides and angles depending on their characteristics.

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Source: Math Hello Kitty
Categories: Math