Finding the Area of the Trapezoid

Oct 13, 2025 by talynt.org 87 views

Introduction

In this article, we will learn how to plot points on a graph sheet, join lines between the points, and find the area of the resulting figure. We will use the points A (5, 5) and B (-5, 5) to demonstrate this process.

Plotting Points A and B

To plot a point on a graph sheet, we need to know its coordinates. The coordinates of a point are given in the form (x, y), where x is the horizontal distance from the origin (0, 0) and y is the vertical distance from the origin.

Let's plot the points A (5, 5) and B (-5, 5) on a graph sheet.

To plot point A (5, 5), we start at the origin (0, 0) and move 5 units to the right and 5 units up. The point A is located at (5, 5).
To plot point B (-5, 5), we start at the origin (0, 0) and move 5 units to the left and 5 units up. The point B is located at (-5, 5).

Joining Lines OA, OB, and BA

Now that we have plotted the points A and B, we can join the lines OA, OB, and BA.

To join line OA, we start at point A (5, 5) and move to the origin (0, 0).
To join line OB, we start at point B (-5, 5) and move to the origin (0, 0).
To join line BA, we start at point B (-5, 5) and move to point A (5, 5).

Naming the Figure

The figure obtained by joining the lines OA, OB, and BA is a trapezoid.

Properties of a Trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides. In this case, the parallel sides are OA and OB.

Finding the Area of the Trapezoid

To find the area of the trapezoid, we need to know the lengths of the parallel sides and the height of the trapezoid.

The length of side OA is 10 units (5 units to the right of the origin and 5 units up).
The length of side OB is 10 units (5 units to the left of the origin and 5 units up).
The height of the trapezoid is 10 units (the distance between the parallel sides).

Formula for the Area of a Trapezoid

The formula for the area of a trapezoid is:

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

Calculating the Area

Substituting the values into the formula, we get:

Area = (1/2) × (10 + 10) × 10 Area = (1/2) × 20 × 10 Area = 100 square units

Conclusion

In this article, we learned how to plot points on a graph sheet, join lines between the points, and find the area of the resulting figure. We used the points A (5, 5) and B (-5, 5) to demonstrate this process and found that the area of the resulting trapezoid is 100 square units.

Key Takeaways

To plot a point on a graph sheet, we need to know its coordinates.
To join lines between points, we need to know the coordinates of the points.
The formula for the area of a trapezoid is (1/2) × (sum of the lengths of the parallel sides) × height.
The area of a trapezoid can be calculated using the formula.

Practice Problems

Plot the points C (3, 2) and D (-3, 2) on a graph sheet. Join the lines OC, OD, and CD. Name the figure obtained and find the area of the figure.
Plot the points E (4, 1) and F (-4, 1) on a graph sheet. Join the lines OE, OF, and EF. Name the figure obtained and find the area of the figure.

Answer Key

The figure obtained is a trapezoid with an area of 20 square units.
The figure obtained is a trapezoid with an area of 20 square units.
Q&A: Plotting Points and Finding the Area of a Trapezoid =====================================================

Frequently Asked Questions

In this article, we will answer some frequently asked questions about plotting points and finding the area of a trapezoid.

Q: What is a trapezoid?

A trapezoid is a quadrilateral with one pair of parallel sides.

Q: How do I plot a point on a graph sheet?

To plot a point on a graph sheet, you need to know its coordinates. The coordinates of a point are given in the form (x, y), where x is the horizontal distance from the origin (0, 0) and y is the vertical distance from the origin.

Q: How do I join lines between points?

To join lines between points, you need to know the coordinates of the points. You can use a ruler or a straightedge to draw a line between the points.

Q: What is the formula for the area of a trapezoid?

The formula for the area of a trapezoid is:

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

Q: How do I calculate the area of a trapezoid?

To calculate the area of a trapezoid, you need to know the lengths of the parallel sides and the height of the trapezoid. You can use the formula above to calculate the area.

Q: What is the difference between a trapezoid and a rectangle?

A trapezoid is a quadrilateral with one pair of parallel sides, while a rectangle is a quadrilateral with two pairs of parallel sides.

Q: Can a trapezoid have more than one pair of parallel sides?

No, a trapezoid by definition has only one pair of parallel sides.

Q: Can a trapezoid be a right triangle?

No, a trapezoid cannot be a right triangle. A right triangle is a triangle with one right angle, while a trapezoid is a quadrilateral with one pair of parallel sides.

Q: Can a trapezoid be a square?

No, a trapezoid cannot be a square. A square is a quadrilateral with four right angles and four equal sides, while a trapezoid is a quadrilateral with one pair of parallel sides.

Q: How do I find the area of a trapezoid with a height of 0?

If the height of a trapezoid is 0, then the area of the trapezoid is 0.

Q: Can a trapezoid have a negative area?

No, a trapezoid cannot have a negative area. The area of a trapezoid is always a positive number.

Conclusion

In this article, we answered some frequently asked questions about plotting points and finding the area of a trapezoid. We hope that this article has been helpful in understanding the concepts of plotting points and finding the area of a trapezoid.

Key Takeaways

A trapezoid is a quadrilateral with one pair of parallel sides.
To plot a point on a graph sheet, you need to know its coordinates.
To join lines between points, you need to know the coordinates of the points.
The formula for the area of a trapezoid is (1/2) × (sum of the lengths of the parallel sides) × height.
The area of a trapezoid can be calculated using the formula.

Practice Problems

Plot the points G (2, 3) and H (-2, 3) on a graph sheet. Join the lines OG, OH, and GH. Name the figure obtained and find the area of the figure.
Plot the points I (4, 2) and J (-4, 2) on a graph sheet. Join the lines OI, OJ, and IJ. Name the figure obtained and find the area of the figure.

Answer Key

The figure obtained is a trapezoid with an area of 20 square units.
The figure obtained is a trapezoid with an area of 20 square units.