Finding the Area Using Two Copies of the Trapezium

Transcript

Finding the Area Using Two Copies of the TrapeziumThere is another interesting way of finding the area of a trapezium. It’s called the Two copies Method, let’s see how we do it Two Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 1 OF 6 Two Copies of the Trapezium Start with trapezium ABCD (blue). Let's take a second, identical copy (green) . Let the top base be a and the bottom base be b. Previous Next StepTwo Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 2 OF 6 Rotate the Second Copy Rotate the second copy by . Notice how the top base a and bottom base switch places. The interior angles and are now on the left edge. Previous Next Step Two Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 3 OF 6 Join Along the Edge BC Slide the second trapezium over so that its left edge ( ) joins perfectly with the right edge (BC) of the first trapezium. Previous Next StepTwo Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 4 OF 6 Are the Edges Straight? Look at the top and bottom junctions. Since AB I DC originally, the interior angles . Therefore, the joined top edge (A-B-D') and bottom edge (D-C-A') form perfectly straight lines! The new shape is a quadrilateral. Previous Next StepTwo Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 5 OF 6 Identifying the Parallelogram Now look at the far left and right edges. Since angles , the left side AD is parallel to the right side . A quadrilateral with straight, parallel opposite sides is a Parallelogram. Previous Next StepTwo Copies Method Finding the area of a trapezium by duplicating, rotating, and joining it to form a parallelogram. STEP 6 OF 6 Area of the Trapezium The base of this massive Parallelogram is . Its height is . Area of Parallelogram . Since it's made of exactly two identical trapeziums, the area of one trapezium is exactly half of that! Area of the trapezium × Area of parallelogram Previous Restart Visualization