Lesson 2 Part 1
When you connect three lines at each end of the lines, they form a triangle. Such closed figures that have three or more sides are called polygons.
Each corner of a polygon is called a vertex. Polygons are classified by the number of sides. A polygon that has four sides is called a quadrilateral.
If each angle of a polygon is the same measure, it is called an equiangular polygon. A rectangle is an equiangular polygon because its four angles are all 90 degrees.
A polygon whose sides are all the same length is called an equilateral polygon.
If an equiangular polygon is also equilateral, it is called a regular polygon. A square is one of the regular polygons because its four sides are equal in length and its four angles are also equal (90 degrees).
Each corner of a polygon is called a vertex. Polygons are classified by the number of sides. A polygon that has four sides is called a quadrilateral.
If each angle of a polygon is the same measure, it is called an equiangular polygon. A rectangle is an equiangular polygon because its four angles are all 90 degrees.
A polygon whose sides are all the same length is called an equilateral polygon.
If an equiangular polygon is also equilateral, it is called a regular polygon. A square is one of the regular polygons because its four sides are equal in length and its four angles are also equal (90 degrees).
Lesson 2 Part 1-1
When you connect three lines at each end of the lines, they form a triangle.
Lesson 2 Part 1-2
Such closed figures that have three or more sides are called polygons.
Lesson 2 Part 1-3
Each corner of a polygon is called a vertex.
Lesson 2 Part 1-4
Polygons are classified by the number of sides.
Lesson 2 Part 1-5
A polygon that has four sides is called a quadrilateral.
Lesson 2 Part 1-6
If each angle of a polygon is the same measure, it is called an equiangular polygon.
Lesson 2 Part 1-7
A rectangle is an equiangular polygon because its four angles are all 90 degrees.
Lesson 2 Part 1-8
A polygon whose sides are all the same length is called an equilateral polygon.
Lesson 2 Part 1-9
If an equiangular polygon is also equilateral, it is called a regular polygon.
Lesson 2 Part 1-10
A square is one of the regular polygons because its four sides are equal in length and its four angles are also equal (90 degrees).
Lesson 2 Part 2
The area of a figure means the number of unit squares that the figure contains. You can find the area of a parallelogram by calculating base times height.
Choose one side of a parallelogram as the base. Then draw a line from another side that is parallel to the base so that the line is perpendicular to the base. The length of the line is its height.
How can you find the area of a triangle?
Choose one side of a triangle as the base. Then draw a line from the vertex opposite to the base so that the line is perpendicular to the base. The length of the line is its height. The product of the base and the height is equal to the area of a parallelogram that has the same base and height. Therefore the area of the triangle is half the area of the parallelogram. So the area of a triangle is base times height divided by two.
Choose one side of a parallelogram as the base. Then draw a line from another side that is parallel to the base so that the line is perpendicular to the base. The length of the line is its height.
How can you find the area of a triangle?
Choose one side of a triangle as the base. Then draw a line from the vertex opposite to the base so that the line is perpendicular to the base. The length of the line is its height. The product of the base and the height is equal to the area of a parallelogram that has the same base and height. Therefore the area of the triangle is half the area of the parallelogram. So the area of a triangle is base times height divided by two.
Lesson 2 Part 2-1
The area of a figure means the number of unit squares that the fi gure contains.
Lesson 2 Part 2-2
You can find the area of a parallelogram by calculating base times height.
Lesson 2 Part 2-3
Choose one side of a parallelogram as the base.
Lesson 2 Part 2-4
Then draw a line from another side that is parallel to the base so that the line is perpendicular to the base.
Lesson 2 Part 2-5
The length of the line is its height.
Lesson 2 Part 2-6
How can you find the area of a triangle?
Lesson 2 Part 2-7
Choose one side of a triangle as the base.
Lesson 2 Part 2-8
Then draw a line from the vertex opposite to the base so that the line is perpendicular to the base.
Lesson 2 Part 2-9
The length of the line is its height.
Lesson 2 Part 2-10
The product of the base and the height is equal to the area of a parallelogram that has the same base and height.
Lesson 2 Part 2-11
Therefore the area of the triangle is half the area of the parallelogram.
Lesson 2 Part 2-12
So the area of a triangle is base times height divided by two.
Lesson 2 Part 3
A circle is the set of all points at a given distance from a fixed point. The fixed point is called the center of the circle. The distance between the center and each point of the circle is called the radius. Draw a line from one point on a circle to another so that it passes through the center. The length of the line is the diameter. The diameter is twice the radius of the circle.
The distance around the circle is the circumference. You can find the circumference of a circle by multiplying its diameter by a fixed constant called “pi”. Pi is also used to find the area of a circle. It is the square of the radius multiplied by pi. Pi is often approximated as 3.14.
The distance around the circle is the circumference. You can find the circumference of a circle by multiplying its diameter by a fixed constant called “pi”. Pi is also used to find the area of a circle. It is the square of the radius multiplied by pi. Pi is often approximated as 3.14.
Lesson 2 Part 3-1
A circle is the set of all points at a given distance from a fixed point.
Lesson 2 Part 3-2
The fixed point is called the center of the circle.
Lesson 2 Part 3-3
The distance between the center and each point of the circle is called the radius.
Lesson 2 Part 3-4
Draw a line from one point on a circle to another so that it passes through the center.
Lesson 2 Part 3-5
The length of the line is the diameter.
Lesson 2 Part 3-6
The diameter is twice the radius of the circle.
Lesson 2 Part 3-7
The distance around the circle is the circumference.
Lesson 2 Part 3-8
You can find the circumference of a circle by multiplying its diameter by a fixed constant called “pi”.
Lesson 2 Part 3-9
Pi is also used to find the area of a circle.
Lesson 2 Part 3-10
It is the square of the radius multiplied by pi.
Lesson 2 Part 3-11
Pi is often approximated as 3.14.
Lesson 2 Part 4
Prisms and cylinders are space figures, or solids, with two bases. Pyramids and cones are solids with one base.
A triangular prism has two bases, which are congruent triangles. It has three lateral faces, which are all rectangles.
If a prism’s bases and lateral faces are all congruent squares, it is called a cube.
A cylinder has two congruent circular faces on its top and bottom, and one curved face around its side.
A pyramid has one base and several triangular lateral faces. If the base is a triangle, it is called a triangular pyramid. If the base is a circle, it is not a pyramid but a cone.
A triangular prism has two bases, which are congruent triangles. It has three lateral faces, which are all rectangles.
If a prism’s bases and lateral faces are all congruent squares, it is called a cube.
A cylinder has two congruent circular faces on its top and bottom, and one curved face around its side.
A pyramid has one base and several triangular lateral faces. If the base is a triangle, it is called a triangular pyramid. If the base is a circle, it is not a pyramid but a cone.
Lesson 2 Part 4-1
Prisms and cylinders are space figures, or solids, with two bases.
Lesson 2 Part 4-2
Pyramids and cones are solids with one base.
Lesson 2 Part 4-3
A triangular prism has two bases, which are congruent triangles.
Lesson 2 Part 4-4
It has three lateral faces, which are all rectangles.
Lesson 2 Part 4-5
If a prism’s bases and lateral faces are all congruent squares, it is called a cube.
Lesson 2 Part 4-6
A cylinder has two congruent circular faces on its top and bottom, and one curved face around its side.
Lesson 2 Part 4-7
A pyramid has one base and several triangular lateral faces.
Lesson 2 Part 4-8
If the base is a triangle, it is called a triangular pyramid.
Lesson 2 Part 4-9
If the base is a circle, it is not a pyramid but a cone.
Lesson 2 Part 5
You can find the volume of a prism or a cylinder by multiplying its base area by its height. The cylinder shown in Figure 1 has two circular bases whose radius is 5 cm. So its base area is 25pi cm2. Then, as the cylinder’s height is 9 cm, its volume is 9 × 25pi = 225pi (cm3).
The volume of a pyramid is one third the volume of a prism that has the same base area and height. The volume of a cone is also one third the volume of a cylinder with the same base area and height. The cone shown in Figure 2 has the same base area and height as the cylinder above. As the volume of the cone is one third the cylinder’s volume, it is 225pi × 1/3 = 75pi (cm3).
The volume of a pyramid is one third the volume of a prism that has the same base area and height. The volume of a cone is also one third the volume of a cylinder with the same base area and height. The cone shown in Figure 2 has the same base area and height as the cylinder above. As the volume of the cone is one third the cylinder’s volume, it is 225pi × 1/3 = 75pi (cm3).
Lesson 2 Part 5-1
You can find the volume of a prism or a cylinder by multiplying its base area by its height.
Lesson 2 Part 5-2
The cylinder shown in Figure 1 has two circular bases whose radius is 5 cm.
Lesson 2 Part 5-3
So its base area is 25pi cm2.
Lesson 2 Part 5-4_1
Then, as the cylinder’s height is 9 cm.
Lesson 2 Part 5-4_2
Its volume is 9 × 25pi = 225pi (cm3).
Lesson 2 Part 5-4
Then, as the cylinder’s height is 9 cm, its volume is 9 × 25pi = 225pi (cm3).
Lesson 2 Part 5-5
The volume of a pyramid is one third the volume of a prism that has the same base area and height.
Lesson 2 Part 5-6
The volume of a cone is also one third the volume of a cylinder with the same base area and height.
Lesson 2 Part 5-7
The cone shown in Figure 2 has the same base area and height as the cylinder above.
Lesson 2 Part 5-8
As the volume of the cone is one third the cylinder’s volume.
Lesson 2 Part 5-9
It is 225pi × 1/3 = 75pi (cm3).