Area of a parallelogram | Perimeter, area, and volume | Geometry | Khan Academy

TL;DR

The area of any parallelogram can be calculated by multiplying one of its bases by the height.

Transcript

We know that quadrilateral ABCD over here is a parallelogram. And what I want to discuss in this video is a general way of finding the area of a parallelogram. In the last video, we talked about a particular way of finding the area of a rhombus. You could take half the product of its diagonals. And a rhombus is a parallelogram. But you can't just g... Read More

Key Insights

• 🙃 The opposite sides of a parallelogram are parallel and congruent.
• 🫤 A parallelogram can be split into two congruent triangles by drawing a diagonal.
• 🟰 The area of a parallelogram is equal to twice the area of one of these triangles.
• ✖️ To find the area of a parallelogram, multiply the length of one of its bases by the height.
• ⚾ The height of a parallelogram can be determined by drawing an altitude perpendicular to the base.
• ⚾ The area of a parallelogram can also be calculated by multiplying the length of a different base by the corresponding height.
• 🔺 The formula for the area of a triangle, 1/2 * base * height, can be applied to find the area of one of the triangles formed by the diagonal.

Questions & Answers

Q: How do you determine if a quadrilateral is a parallelogram?

A quadrilateral is a parallelogram if its opposite sides are parallel and congruent.

Q: How can you find the area of a parallelogram?

To find the area of a parallelogram, you can multiply the length of one of its bases by the height.

Q: What is the relationship between the areas of the two congruent triangles formed by the diagonal of a parallelogram?

The areas of the two triangles formed by the diagonal of a parallelogram are equal.

Q: Can you calculate the area of any parallelogram using the diagonal?

No, the area of a parallelogram cannot be calculated by halving the product of its diagonals, as is done with a rhombus. Instead, the area can be found by multiplying a base by the height.

Summary & Key Takeaways

• A parallelogram is a quadrilateral with opposite sides that are parallel and congruent.

• By drawing a diagonal in a parallelogram, we can split it into two congruent triangles.

• The area of a parallelogram is equal to twice the area of one of these triangles, which can be calculated using the formula: 1/2 * base * height.