Section: 三角三角三角区域 | 9.12 三角地区

Section outline

Three kids form the Tri-County Dance Team. They are painting a triangular shaped logo on their T-shirts and want the base to be 6 inches long and the height 4 inches. How many square inches of fabric paint do they need for three shirts?
::三个孩子组成了三角舞蹈队。他们在T恤上画三角形标志,希望基地长6英寸,高4英寸。三件衬衫需要多少平方英寸的布料涂料?

In this concept, you will learn how to find the area of any triangle when the base and height are given.
::在此概念中, 当给定基数和高度时, 您将学会如何找到任何三角形的区域。

Finding the Area of a Triangle
::查找三角区域

A triangle is a three sided figure made up of three sides and three angles . The area of a triangle is related to the area of a . The formula for finding the area of a parallelogram, $\begin{aligned} A = b h \end{aligned}$ .
::三角形是一个由三面和三个角度组成的三个侧形图。三角形区域与一个区域有关。查找平行图区域的公式为A=bh。

Notice that the parallelogram above has been divided into two triangles. Each triangle equals one half of the parallelogram. The formula for the area of a triangle is one half the area of a parallelogram.
::请注意上面的平行图已被分为两个三角形。每个三角形等于平行图的一半。三角形区域的公式是平行图区域的一半。

The formula can be written: $\begin{aligned} A = \frac{1}{2} b h or A = \frac{b h}{2} \end{aligned}$
::公式可以写为: A=12 bh 或 A=bh2。

Let's look at an example. Find the area of the triangle.
::让我们举个例子,找出三角形的面积

First, write the formula.
::首先,写公式。

$\begin{aligned} A = \frac{1}{2} b h \end{aligned}$

::A=12bh =12bh

Next, insert the given values.
::下一步插入给定值。

$\begin{aligned} A = \frac{1}{2} (11) (16) \end{aligned}$
::A=12(11)(16)

Then express all terms as fractions and multiply.
::然后,以分数和乘数表示所有条件。

$\begin{aligned} \begin{array}{rcl} A & = & (\frac{1}{2}) (\frac{11}{1}) (\frac{16}{1}) \\ A & = & 88 s q c m \end{array} \end{aligned}$

::A=( 12) (111) (161) A=88 sq cm

The answer is 88 sq. cm.
::答案是88平方米厘米

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about the Tri-County Dance Team and their triangular logo.
::早些时候,你被问及三州舞蹈队和他们的三角标志的问题。

They need to buy enough fabric paint for three triangles that measure 6 inches at the base and are 4 inches high. The paint that they buy should cover how many square feet?
::他们需要为三个三角买足够的布料涂料,三个三角形在基座上测量6英寸,高4英寸。他们购买的涂料应该覆盖多少平方英尺?

First, write the formula.
::首先,写公式。

$\begin{aligned} A = \frac{b h}{2} \end{aligned}$

::A=bh2 阿=bh2

Next, fill in the values that you are given.
::下一步,填入给定的值。

$\begin{aligned} A = \frac{(6) (4)}{2} \end{aligned}$
::A=(6)(4)2

Then, do the arithmetic.
::那就算算吧算算吧算算啊算算啊算算啊算啊算啊

$\begin{aligned} A = 12 s q i n \end{aligned}$
::A=12 平方英寸

Remember, there are three shirts, so multiply by 3.
::记住,有三件衬衫所以乘以三

$\begin{aligned} 12 \times 3 = 36 \end{aligned}$

The answer is 36 sq. in. The team needs enough paint to cover 36 square inches.
::答案是36平方英寸摄制组需要足够的油漆覆盖36平方英寸

Example 2
::例2

What is the area of the triangle below?
::下面三角形的面积是多少?

First, write the formula.
::首先,写公式。

$\begin{aligned} A = \frac{1}{2} b h \end{aligned}$

::A=12bh =12bh

Next, insert the given values.
::下一步插入给定值。

$\begin{aligned} A = \frac{1}{2} (17) (5) \end{aligned}$
::A=12(17)(5)

Then, express all terms as fractions and multiply.
::然后,你应当以百分数和乘数来表达万物。

$\begin{aligned} \begin{array}{rcl} A & = & (\frac{1}{2}) (\frac{17}{1}) (\frac{5}{1}) \\ A & = & 42.5 s q c m \end{array} \end{aligned}$

::A=12(171)(51)A=42.5平方公里

The answer is 42.5 sq. cm.
::答案是42.5平方米cm

Example 3
::例3

A triangle has a base of $\begin{aligned} 9^{''} \end{aligned}$ and a height of $\begin{aligned} 4^{''} \end{aligned}$ . What is its area?
::三角形的基数为 9, 高度为 4。其区域是什么 ?

First, write the formula.
::首先,写公式。

$\begin{aligned} A = \frac{b h}{2} \end{aligned}$

::A=bh2 阿=bh2

Next, fill in the values that you are given.
::下一步,填入给定的值。

$\begin{aligned} A = \frac{(9) (4)}{2} \end{aligned}$
::A=(9)(4)2

Then, do the arithmetic.
::那就算算吧算算吧算算啊算算啊算算啊算啊算啊

$\begin{aligned} A = 18 s q i n \end{aligned}$
::A=18 平方英寸

The answer is 18 sq. in.
::答案是18平方米英寸英寸

Example 4
::例4

Find the area of a triangle that has a base = 11 inches and a height = 7 inches.
::查找三角形区域,其基数为 11 英寸,高度为 7 英寸。

First, write the formula.
::首先,写公式。

$\begin{aligned} A = \frac{b h}{2} \end{aligned}$

::A=bh2 阿=bh2

Next, fill in the values that you are given.
::下一步,填入给定的值。

$\begin{aligned} A = \frac{(11) (7)}{2} \end{aligned}$
::A=(11)(7)2

Then, do the arithmetic.
::那就算算吧算算吧算算啊算算啊算算啊算啊算啊

$\begin{aligned} A = 38.5 s q i n \end{aligned}$
::A=38.5平方米英寸

The answer is 38.5 sq. in.
::答案是38.5平方米英寸

Review
::回顾

Find the area of each triangle given the base and height.
::根据基数和高度查找每个三角形的区域。

Base = 9 in, height = 4 in
::基数=9英寸,身高=4英寸

Base = 6 in, height = 3 in
::基数=6英寸,高度=3英寸

Base = 7 in, height = 4 in
::基数=7英寸,身高=4英寸

Base = 9 m, height = 7 m
::基数=9米,高度=7米

Base = 12 ft, height = 10 feet
::基数 = 12英尺,高度 = 10英尺

Base = 14 feet, height = 5 feet
::基地=14英尺,高度=5英尺

Base = 14 feet, height = 13 feet
::基地=14英尺,高度=13英尺

Base = 11 meters, height = 8 meters
::基地=11米,高度=8米

Base = 13 feet, height = 8.5 feet
::基地=13英尺,高度=8.5英尺

Base = 11.5 meters, height = 9 meters
::基地=11.5米,高度=9米

Base = 18 meters, height = 15 meters
::基地=18米,高度=15米

Base = 21 feet, height = 15.5 feet
::基地=21英尺,高度=15.5英尺

Base = 18 feet, height = 11 feet
::基地=18英尺,高度=11英尺

Base = 20.5 meters, height = 15.5 meters
::基地=20.5米,高度=15.5米

Base = 40 feet, height = 22 feet
::基地=40英尺,高度=22英尺

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

Finding the Area of a Triangle ::查找三角区域

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Finding the Area of a Triangle
::查找三角区域

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源