In this lesson, students learn how to determine the area of a parallelogram. Three types of parallelograms are covered: squares, rectangles, and regular parallelograms.
The area of a parallelogram is defined as the area of the base times the height. The height is measured perpendicular to the height. The result is the number of square units in the parallelogram.
In an earlier lesson, students learned that the area of a rectangle is the product of the width of the rectangle times the length of the rectangle. In this lesson the students make use of that knowledge to learn how to find the area of a triangle.
Any given rectangle can be divided into two equal triangles by drawing a line that connects any two opposite corners. That means that the area of a rectangle is equal to twice the area of each of these triangles. The area of either triangle is one half the area of the rectangle.
This is used as the basis for defining the area of a right triangle. The length of one side adjacent the right angle times is the length and the length of the other side adjacent the right angle is the width. The area of the triangle is the product of the length times the width times one-half.
Any given parallelogram can also be divided into two equal triangles by drawing a line that connects any two opposite corners. That means that the area of a parallelogram is equal to twice the area of each of these triangles. The area of either triangle is one half the area of the rectangle.
This is used as a basis for defining the area of a triangle in general. The area of a triangle is the one-half the area of the corresponding parallelogram, where the area of the parallelogram is the base of the parallelogram times the height of the parallelogram, measured perpendicular to the base.
This definition applies to all triangles, acute, obtuse and right triangles.
In earlier lessons, students have learned how to find the volume of a rectangular prism when the lengths of the sides are whole numbers. Subsequently, they have learned to use decimal numbers.
In this lesson, they extend the knowledge of volume to calculate the volume of a rectangular prism when the lengths of the sides are decimal numbers.
In earlier lessons, students learned how to find the area of a flat surface.
In this lesson, students extend that knowledge to learn how to find the surface area of a three-dimensional figure. Surface area is defined as the number of square units on the outside of a figure. It’s the sum of the area of each flat surface, or face, of a three-dimensional figure.
A rectangular prism (a box) has six flat surfaces. For any rectangular prism, there are always three pairs of opposite surfaces that have the same area. The surface area is the sum of the areas of each of these six surfaces, or three times the sum of the area of opposite sides.
Since the surface area is a sum of the area of multiple flat surfaces, the area is expressed in square units.