Students have been learning a lot about geometry. First, they learned about types of angles and pairs of angles. They were able to use what they learned about angles to determine the measures of given angles in different situations. Next, they learned about polygons. Students learned how to identify polygons based on their characteristics. They also learned how to tell if two polygons are similar, as well as how to determine the missing lengths in similar polygons.
Students are now finding the areas of parallelograms, triangles, and trapezoids. Starting with parallelograms, students cut out parallelograms and cut along their heights to create a trapezoid and a triangle. By rearranging the pieces, they were able to make a rectangle. Using what they already know about the area of a rectangle, students saw that the area of a parallelogram is found the same way by multiplying the length of the base by the length of the height. Next, students looked at triangles. Unable to cut a rearrange a triangle to create a different shape, students instead cut out two triangles. Placing them together, they saw that they created a parallelogram. Because the original triangle is only half the size of this new parallelogram, they get the area of the triangle by multiplying the length of the base by the length of the height and then dividing by two. Similarly with a trapezoid, students were able to create a parallelogram by placing two identical trapezoids together. The base of the parallelogram created was the sum of the two bases of the trapezoid, so the area of the trapezoid is this sum times the height of the trapezoid divided by two.
Students are now finding the areas of parallelograms, triangles, and trapezoids. Starting with parallelograms, students cut out parallelograms and cut along their heights to create a trapezoid and a triangle. By rearranging the pieces, they were able to make a rectangle. Using what they already know about the area of a rectangle, students saw that the area of a parallelogram is found the same way by multiplying the length of the base by the length of the height. Next, students looked at triangles. Unable to cut a rearrange a triangle to create a different shape, students instead cut out two triangles. Placing them together, they saw that they created a parallelogram. Because the original triangle is only half the size of this new parallelogram, they get the area of the triangle by multiplying the length of the base by the length of the height and then dividing by two. Similarly with a trapezoid, students were able to create a parallelogram by placing two identical trapezoids together. The base of the parallelogram created was the sum of the two bases of the trapezoid, so the area of the trapezoid is this sum times the height of the trapezoid divided by two.