In Saxon Math Course 1, Lesson 71 introduces Grade 6 students to key properties of parallelograms, including opposite angles being equal, adjacent angles being supplementary, and how to calculate area using the formula base times height. Students explore why this area formula works by cutting and rearranging a parallelogram into a rectangle with equivalent dimensions. The lesson also examines how a parallelogram's area changes as its angles change while its side lengths remain constant.
Section 1
📘 Parallelograms
A parallelogram is a quadrilateral with two pairs of parallel sides. Its area is found by multiplying the base by the height, as shown in the formula:
This is just the foundation. Next, you'll walk through worked examples to calculate the area, perimeter, and unknown angles of different parallelograms.
Section 2
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite angles are equal, and adjacent angles are supplementary (their sum is ).
In parallelogram , if , then its opposite angle .
If , its adjacent angle must be .
If in a parallelogram, its opposite angle is and its adjacent angles are both .
Imagine a rectangle getting a playful push! The sides stay parallel, but the angles tilt. This new shape is a parallelogram. A key secret is that the corners directly across from each other always stay identical twins (equal angles). Meanwhile, any two corners next to each other have to team up to make a perfect !
Section 3
Area of a Parallelogram
To find the area of a parallelogram, we multiply the base by the height. The formula is , where is the length of one side (the base) and is the perpendicular distance to the opposite side (the height).
A parallelogram with a base of 10 cm and a height of 5 cm has an area of sq. cm.
A parallelogram has a base of 8 inches and a height of 4 inches, so its area is sq. in.
If a parallelogram's area is 48 sq. meters and its base is 12 meters, the height is meters.
Finding a parallelogram's area seems tricky, but it's a magic trick! Just snip a triangle off one end, slide it to the other, and voilà —you’ve made a rectangle. Since you only moved a piece, the area is exactly the same! Now, just multiply the base by the height, which were the length and width of your new rectangle.
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Section 1
📘 Parallelograms
A parallelogram is a quadrilateral with two pairs of parallel sides. Its area is found by multiplying the base by the height, as shown in the formula:
This is just the foundation. Next, you'll walk through worked examples to calculate the area, perimeter, and unknown angles of different parallelograms.
Section 2
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite angles are equal, and adjacent angles are supplementary (their sum is ).
In parallelogram , if , then its opposite angle .
If , its adjacent angle must be .
If in a parallelogram, its opposite angle is and its adjacent angles are both .
Imagine a rectangle getting a playful push! The sides stay parallel, but the angles tilt. This new shape is a parallelogram. A key secret is that the corners directly across from each other always stay identical twins (equal angles). Meanwhile, any two corners next to each other have to team up to make a perfect !
Section 3
Area of a Parallelogram
To find the area of a parallelogram, we multiply the base by the height. The formula is , where is the length of one side (the base) and is the perpendicular distance to the opposite side (the height).
A parallelogram with a base of 10 cm and a height of 5 cm has an area of sq. cm.
A parallelogram has a base of 8 inches and a height of 4 inches, so its area is sq. in.
If a parallelogram's area is 48 sq. meters and its base is 12 meters, the height is meters.
Finding a parallelogram's area seems tricky, but it's a magic trick! Just snip a triangle off one end, slide it to the other, and voilà —you’ve made a rectangle. Since you only moved a piece, the area is exactly the same! Now, just multiply the base by the height, which were the length and width of your new rectangle.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter