# Lesson 2 Homework Practice Area Of Triangles Answers To Math

**Note:**

- Before this lesson I
**Post A Key.**

I have a student read over the directions. I review expectations and students start working independently. Students are engaging in **MP2: Reason abstractly****and quantitatively, MP6: Attend to precision, MP7: Look for and make use of structure**.

As students work I walk around to monitor student progress and behavior. If students are struggling, I may ask them one or more of the following questions:

- How can we identify the base and height of a triangle?
- What are the base and height of the triangle? How do you know?
- How can you find the area of a triangle? Why does that work?
- Which of these triangles have the same area? How can that be?

When students complete their work, they raise their hands. I quickly scan their work. If they are on track, I send them to check with the key. If there are problems, I tell students what they need to revise. If students successfully complete the chart they can work on the challenge question.

The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug. A **triangle** is a three-sided polygon. We will look at several types of triangles in this lesson.

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

Since the area of a parallelogram is A = B * H, the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is:

or

where b is the base, h is the height and **·** means multiply.

The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.

Example 1: Find the area of an acute triangle with a base of 15 inches and a height of 4 inches.

Solution:

= **·** (15 in) **·** (4 in)

** = ****·** (60 in^{2})

= 30 in^{2}

Example 2: Find the area of a right triangle with a base of 6 centimeters and a height of 9 centimeters.

Solution:

= **·** (6 cm) **·** (9 cm)

** = ****·** (54 cm^{2})

= 27 cm^{2}

Example 3: Find the area of an obtuse triangle with a base of 5 inches and a height of 8 inches.

Solution:

= **·** (5 in) **·** (8 in)

** = ****·** (40 in^{2})

= 20 in^{2}

Example 4: The area of a triangle shaped mat is 18 square feet and the base is 3 feet. Find the height. *(Note: The triangle in the illustration to the right is NOT drawn to scale.)*

Solution:

In this example, we are given the area of a triangle and one dimension, and we are asked to work backwards to find the other dimension.

18 ft^{2} = \B7 (3 ft) **· **h

Multiplying both sides of the equation by 2, we get:

36 ft^{2} = (3 ft) **· **h

Dividing both sides of the equation by 3 ft, we get:

12 ft = h

Commuting this equation, we get:

h = 12 ft

Summary: Given the base and the height of a triangle, we can find the area. Given the area and either the base or the height of a triangle, we can find the other dimension. The formula for area of a triangle is:

or where b is the base and h is the height.

**Exercises**

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Your answers should be given as whole numbers greater than zero. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. | Find the area of a triangle with a base of 16 feet and a height of 3 feet. |

2. | Find the area of a triangle with a base of 4 meters and a height of 14 meters. |

3. | Find the area of a triangle with a base of 18 inches and a height of 2 inches. |

4. | A triangle shaped piece of paper has an area of 36 square centimeters and a base of 6 centimeters. Find the height. (Hint: work backwards) |

5. | The area of a triangle shaped rug is 12 square yards and the height is 3 yards. Find the base. (Hint: work backwards) |

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