Class 9 Exam > Class 9 Notes > Theory - To Show that the Area of a Triangle is half the product of the Base and the Height, Math
Theory - To Show that the Area of a Triangle is half the product of the Base and the Height, Math - Class 9 PDF Download
Objective:
To show that the area of a triangle is half the product of the base and the height.
Theory:
Triangle: A triangle is one of the basic shapes in geometry: a polygon with three corners or vertices and three sides or edges which are line segments.
Types of triangles:
Right angled triangle:
A right angled triangle has one of its interior angles measuring 90°. The side opposite to the right angle is the hypotenuse; it is the longest side of the triangle. For a right angled triangle with sides a, b, c where c is the hypotenuse, a2 + b2 = c2.
Acute angled triangle:
A triangle that has all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. For an acute-angled triangle with sides a, b, c where c is the greatest side, a2 + b2 > c2.
Obtuse angled triangle:
A triangle that has one interior angle that measures more than 90° is an obtuse triangle or obtuse-angled triangle. For an obtuse-angled triangle with sides a, b, c where c is the greatest side, a2 + b2 < c2.
FAQs on Theory - To Show that the Area of a Triangle is half the product of the Base and the Height, Math - Class 9
| 1. What is the formula to find the area of a triangle? |  |
Ans. The formula to find the area of a triangle is (1/2) x base x height, where the base is the length of the triangle's base and the height is the perpendicular distance from the base to the opposite vertex.
| 2. Why is the formula for the area of a triangle half the product of the base and height? | |
Ans. The formula for the area of a triangle being half the product of the base and height can be understood by considering that a triangle can be divided into two equal right triangles. Each right triangle has the base and height as its sides, and the area of each right triangle is given by (1/2) x base x height. Therefore, when we add the areas of both right triangles, we get the formula for the area of the whole triangle, which is (1/2) x base x height.
| 3. Can the formula for the area of a triangle be used for all types of triangles? | |
Ans. Yes, the formula for the area of a triangle (1/2) x base x height can be used for all types of triangles, including equilateral, isosceles, and scalene triangles. The only requirement is that the base and height of the triangle are known.
| 4. What if the height of a triangle is not given? Can we still find the area? | |
Ans. If the height of a triangle is not given, it can be calculated using various methods, such as using the Pythagorean theorem, trigonometric ratios, or the lengths of other known sides. Once the height is determined, the area of the triangle can be found using the formula (1/2) x base x height.
| 5. Is the formula for the area of a triangle applicable to three-dimensional figures? | |
Ans. No, the formula for the area of a triangle (1/2) x base x height is only applicable to two-dimensional triangles. For three-dimensional figures, such as pyramids or prisms, the formula for their surface area or volume needs to be used.
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