the area of a triangle is equal to area of a rectangle. Both triangle and rectangle have a common side, its base. If width of rectangle is 6cm, then find height of triangle.
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Answer:
yes this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve. In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.
Solve Geometry Applications.
Answer:
The plural of the word vertex is vertices. All triangles have three vertices. Triangles are named by their vertices: The triangle in (Figure) is called \text{△}ABC.
Triangle ABC has vertices A, B, and C. The lengths of the sides are a, b, and c.
A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively.
The three angles of a triangle are related in a special way. The sum of their measures is 180\text{°}. Note that we read m\text{∠}A as “the measure of angle A.” So in \text{△}ABC in (Figure),
m\text{∠}A+m\text{∠}B+m\text{∠}C=180\text{°}
Because the perimeter of a figure is the length of its boundary, the perimeter of \text{△}ABC is the sum of the lengths of its three sides.
P=a+b+c
To find the area of a triangle, we need to know its base and height. The height is a line that connects the base to the opposite vertex and makes a 90\text{°} angle with the base. We will draw \text{△}ABC again, and now show the height, h. See (Figure).
The formula for the area of \text{△}ABC is A=\frac{1}{2}bh, where b is the base and h is the height.
A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively. The side b is parallel to the bottom of the page, and it has a dashed line drawn from vertex B to it. This line is marked h and makes a right angle with side b.
Triangle Properties
A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively. The side b is parallel to the bottom of the page, and it has a dashed line drawn from vertex B to it. This line is marked h and makes a right angle with side b.
For \text{△}ABC
Angle measures:
m\text{∠}A+m\text{∠}B+m\text{∠}C=180
The sum of the measures of the angles of a triangle is 180\text{°}.