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Chapter 1: Problem 1

Write a formula for the area of a triangle of base \(b\) and height \(h\).

Short Answer

Expert verified
The area of a triangle is \( \frac{1}{2} \times b \times h \).

Step by step solution

01

Identify the variables

Identify the variables in the problem. Here, the base of the triangle is denoted by \(b\), and the height of the triangle is denoted by \(h\).
02

Recall the formula for the area of a triangle

The formula for the area of a triangle is given by \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
03

Substitute the identified variables

Substitute the variables \(b\) for the base and \(h\) for the height into the formula. Thus, the formula becomes \( \text{Area} = \frac{1}{2} \times b \times h \).
04

Simplify the formula if needed

The formula \( \text{Area} = \frac{1}{2} \times b \times h \) is already in its simplest form.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

geometry
Geometry is a branch of mathematics that deals with shapes, sizes, and properties of space. In geometry, we study various figures like circles, squares, and triangles.
Understanding geometric properties is essential in many fields, from engineering to art. For example, when dealing with triangles, we often need to calculate their area using specific formulas.
One such formula involves the base and height of the triangle. Knowing these measurements helps us determine the size of the space inside the triangle.
triangle
A triangle is a three-sided polygon that is one of the simplest shapes in geometry. Triangles are classified based on their side lengths and angles, such as equilateral, isosceles, and scalene triangles.
Each type of triangle has unique properties, but all share a common area formula. The area of a triangle can be calculated if we know the length of its base and its height.
Remember, the base of the triangle can be any one of its sides, and the height is a perpendicular line from that base to the opposite vertex.
mathematical formula
A mathematical formula is a powerful tool that allows us to solve problems quickly and accurately. The formula for the area of a triangle is particularly useful.
The general formula is given by \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\). This formula is derived from the principle that the area of a triangle is half the area of a rectangle with the same base and height.
Using this formula, we can easily find the area once we know the base (\b\text) and the height (\b\text). Simply substitute these values into the formula to compute the area.
algebra
Algebra involves working with variables and symbols to represent numbers and quantities. It helps us formulate equations and solve them systematically.
In the context of the area of a triangle, algebra helps us manipulate the formula to find different values. For example, if we know the area and the height, we can rearrange the formula to find the base, \(\text{base} = \frac{2 \times \text{Area}}{\text{height}}\).
This versatility makes algebra a critical tool in solving geometry problems and finding unknown measurements in triangles and other shapes.

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