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The base of a right-angled triangle is 12 cm and its hypotenuse is 13 cm. What is the area of the triangle?
30 cm┬▓
60 cm┬▓
45 cm┬▓
78 cm┬▓
30 cm┬▓
To find the area of a right-angled triangle, we first calculate the height using the Pythagorean theorem, where the sum of the squares of the two legs equals the square of the hypotenuse. With a base of 12 cm and a hypotenuse of 13 cm, the height is 132тИТ122тАЛ=5 cm, leading to an area of 30 cm2.
To find the area of a right-angled triangle, we first calculate the height using the Pythagorean theorem, where the sum of the squares of the two legs equals the square of the hypotenuse. With a base of 12 cm and a hypotenuse of 13 cm, the height is 132тИТ122тАЛ=5 cm, leading to an area of 30 cm2.
Think of a ladder leaning against a wall; the wall and the ground form the base and height of a right-angled triangle, while the ladder acts as the hypotenuse.
Remember '3-4-5' and '5-12-13' as common Pythagorean triples to save time during exams.
c2=a2+b2 тАФ Pythagorean theorem relating hypotenuse c and legs a,b
Area=21тАЛ├Чb├Чh тАФ formula for the area of a triangle
The Pythagorean theorem, defined as a2+b2=c2, dictates the relationship between sides of a right triangle. The area formula Area=21тАЛ├Чbase├Чheight determines the two-dimensional space bounded by these sides. These principles are fundamental in vector analysis and trigonometry.
A right triangle with sides 5,12,13 is a classic example of a Pythagorean triple.
The hypotenuse is always the longest side in a right-angled triangle.
The area calculation depends strictly on the perpendicular height, not the hypotenuse.
Standardized methodology for geometric measurements
Essential for calculating distances in coordinate geometry
Applicable only to right-angled triangles for this specific formula
Architecture and construction for ensuring perpendicularity
Navigation and GPS coordinate calculations
The height is calculated as 169тИТ144тАЛ=25тАЛ=5 cm.
Option B is 60 cm2, which is obtained by using the hypotenuse as a base, which is mathematically incorrect.
A is correct тАФ The triangle has a height of 5 cm, making the area 21тАЛ├Ч12├Ч5=30 cm2.
Always verify if the given sides form a valid triangle using the triangle inequality theorem before performing calculations.
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