Formula to Solve the Problem

Oct 13, 2025 by vinooalluri.com 128 views

Problem Statement

A rice field is in the shape of a trapezoid, with parallel sides of length 50m and 80m. The distance between the parallel sides is 30m. What is the area of the rice field?

Given Facts

The length of the shorter parallel side (base) is 50m.
The length of the longer parallel side (base) is 80m.
The distance between the parallel sides (height) is 30m.

Formula to Solve the Problem

The formula to find the area of a trapezoid is:

Area = (1/2) × (sum of parallel sides) × height

Solution

To find the area of the rice field, we need to plug in the given values into the formula.

First, we need to find the sum of the parallel sides:

sum of parallel sides = 50m + 80m = 130m

Now, we can plug in the values into the formula:

Area = (1/2) × 130m × 30m Area = (1/2) × 3900m² Area = 1950m²

Therefore, the area of the rice field is 1950 square meters.

Discussion

The problem requires us to find the area of a trapezoid, which is a type of quadrilateral with two parallel sides. The formula to find the area of a trapezoid is given by:

Area = (1/2) × (sum of parallel sides) × height

This formula can be derived by dividing the trapezoid into two triangles and a rectangle. The sum of the areas of these two triangles and the rectangle is equal to the area of the trapezoid.

The solution to the problem involves plugging in the given values into the formula and simplifying the expression. The final answer is the area of the rice field, which is 1950 square meters.

Real-World Applications

The problem of finding the area of a trapezoid has many real-world applications. For example, in architecture, the area of a trapezoid can be used to find the area of a roof or a wall. In engineering, the area of a trapezoid can be used to find the area of a beam or a column.

Conclusion

In conclusion, the problem of finding the area of a trapezoid is a simple yet important problem in mathematics. The formula to find the area of a trapezoid is given by:

Area = (1/2) × (sum of parallel sides) × height

This formula can be used to find the area of a trapezoid in many real-world applications. The solution to the problem involves plugging in the given values into the formula and simplifying the expression. The final answer is the area of the rice field, which is 1950 square meters.

Additional Examples

Here are a few additional examples of finding the area of a trapezoid:

A trapezoid has parallel sides of length 60m and 90m. The distance between the parallel sides is 20m. What is the area of the trapezoid?
A trapezoid has parallel sides of length 40m and 70m. The distance between the parallel sides is 15m. What is the area of the trapezoid?
A trapezoid has parallel sides of length 30m and 50m. The distance between the parallel sides is 10m. What is the area of the trapezoid?

These examples can be solved using the same formula:

Area = (1/2) × (sum of parallel sides) × height

Final Answer

Q: What is the formula to find the area of a trapezoid?

A: The formula to find the area of a trapezoid is:

Area = (1/2) × (sum of parallel sides) × height

Q: How do I find the sum of the parallel sides?

A: To find the sum of the parallel sides, you need to add the lengths of the two parallel sides together.

Q: What if the trapezoid is not a right trapezoid? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid, even if it's not a right trapezoid. However, you need to make sure that the height of the trapezoid is perpendicular to the parallel sides.

Q: Can I use the formula to find the area of a triangle?

A: No, the formula is specifically designed for trapezoids. If you want to find the area of a triangle, you need to use a different formula:

Area = (1/2) × base × height

Q: What if I have a trapezoid with three parallel sides? Can I still use the formula?

A: No, the formula is only applicable to trapezoids with two parallel sides. If you have a trapezoid with three parallel sides, you need to use a different formula or divide the trapezoid into smaller shapes.

Q: Can I use the formula to find the area of a rectangle?

A: Yes, a rectangle is a special type of trapezoid with two parallel sides of equal length. You can use the formula to find the area of a rectangle:

Area = (1/2) × (sum of parallel sides) × height

Q: What if I have a trapezoid with a curved side? Can I still use the formula?

A: No, the formula is only applicable to trapezoids with straight sides. If you have a trapezoid with a curved side, you need to use a different formula or divide the trapezoid into smaller shapes.

Q: Can I use the formula to find the area of a circle?

A: No, the formula is only applicable to trapezoids. If you want to find the area of a circle, you need to use a different formula:

Area = π × radius²

Q: What if I have a trapezoid with a height of zero? Can I still use the formula?

A: No, the formula is only applicable to trapezoids with a non-zero height. If you have a trapezoid with a height of zero, you need to use a different formula or divide the trapezoid into smaller shapes.

Q: Can I use the formula to find the area of a polygon with more than four sides?

A: Yes, you can use the formula to find the area of a polygon with more than four sides, as long as it can be divided into smaller trapezoids.

Q: What if I have a trapezoid with a non-integer height? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a non-integer height. However, you need to make sure that the height is a rational number.

Q: Can I use the formula to find the area of a trapezoid with a negative height?

A: No, the formula is only applicable to trapezoids with a non-negative height. If you have a trapezoid with a negative height, you need to use a different formula or divide the trapezoid into smaller shapes.

Q: What if I have a trapezoid with a height that is not a multiple of the base? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a height that is not a multiple of the base. However, you need to make sure that the height is a rational number.

Q: Can I use the formula to find the area of a trapezoid with a base that is not a multiple of the height?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is not a multiple of the height. However, you need to make sure that the base is a rational number.

Q: What if I have a trapezoid with a base that is a multiple of the height? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height. However, you need to make sure that the base is a rational number.

Q: Can I use the formula to find the area of a trapezoid with a height that is a multiple of the base?

A: Yes, you can still use the formula to find the area of a trapezoid with a height that is a multiple of the base. However, you need to make sure that the height is a rational number.

Q: What if I have a trapezoid with a base that is a multiple of the height and the height is a multiple of the base? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is a multiple of the base. However, you need to make sure that the base and the height are rational numbers.

Q: Can I use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is not a multiple of the base?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is not a multiple of the base. However, you need to make sure that the base is a rational number.

Q: What if I have a trapezoid with a height that is a multiple of the base and the base is not a multiple of the height? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a height that is a multiple of the base and the base is not a multiple of the height. However, you need to make sure that the height is a rational number.

Q: Can I use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is a multiple of the base and the base is a multiple of the height?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is a multiple of the base and the base is a multiple of the height. However, you need to make sure that the base and the height are rational numbers.

Q: What if I have a trapezoid with a base that is not a multiple of the height and the height is not a multiple of the base? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is not a multiple of the height and the height is not a multiple of the base. However, you need to make sure that the base and the height are rational numbers.

Q: Can I use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is not a multiple of the base and the base is not a multiple of the height?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is not a multiple of the base and the base is not a multiple of the height. However, you need to make sure that the base is a rational number.

Q: What if I have a trapezoid with a height that is a multiple of the base and the base is not a multiple of the height and the height is not a multiple of the base? Can I still use the formula?

A: Yes, you can still use the formula to find the area of a trapezoid with a height that is a multiple of the base and the base is not a multiple of the height and the height is not a multiple of the base. However, you need to make sure that the height is a rational number.

Q: Can I use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is a multiple of the base and the base is not a multiple of the height and the height is not a multiple of the base?

A: Yes, you can still use the formula to find the area of a trapezoid with a base that is a multiple of the height and the height is a multiple of the base and the base is not a multiple of the height and the height is not a multiple of the base.