Area of parallelograms and triangles

This is a series of THREE lessons that build on each other where we first learn how to find the area of parallelograms, then the area of right triangles, and lastly the area of triangles.

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Area of parallelograms
Area of right triangles
Area of triangles

Area of parallelograms

Learn WHY the area of a parallelogram is calculated as base times height (altitude).

The formula is A = b × h and it is really simple to prove. If we cut a triangle off of one end of a parallelogram and move it to the other end, we get a RECTANGLE, whose area is the same as the based of the parallelogram times its height.

We also practice finding the areas of parallelograms, and draw a parallelogram with a given area.

This geometry lesson is meant for 6th grade, and is one in a series of lessons on area of polygons. Our next step is the area of right triangles, followed by the area of triangles.

Area of right triangles

This is a lead-up lesson to the lesson about the area of triangles. In this lesson we only deal with RIGHT triangles. It is easy to see their area is HALF of the area of the rectangle drawn around the triangle.

We find the areas of some right triangles and the area of a compound shape. Lastly, the task is to DRAW a right triangle with a given area (300 square centimeters). I show how to find the base and the height for this triangle and draw 2 different ones.

Area of triangles

We learn how the area of any triangle is HALF of the area of the corresponding parallelogram, and that is the reason for the formula A = bh/2 (base times height divided by two).

We also find the area of some triangles that are drawn in the grid.

Area of parallelograms and triangles