Mathematics · Quantitative Aptitude

Triangle Properties

234 Questions

Triangle properties encompass the rules governing the sides, angles, and area of different types of triangles. Key areas include the Pythagorean theorem, similar triangles, and centroid calculations. These concepts form a foundational part of geometry in various competitive examinations.

Similar trianglesArea and perimeterPythagorean theoremTriangle inequalityEquilateral properties

Triangle Properties Questions

Multiple choice

Which formula did Brahmagupta provide for calculating the area of a triangle?

  1. $A = (1/2) * b * h$
  2. $A = b * h$
  3. $A = (1/2) * b^2 * h$
  4. $A = b^2 * h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for calculating the area of a triangle is $A = (1/2) * b * h$, where 'b' is the base and 'h' is the height of the triangle.

Multiple choice

What is the formula for calculating the area of a triangle using sine, as given by Aryabhata?

  1. Area = (1/2) * base * height

  2. Area = (1/2) * base * sine(angle)

  3. Area = base * height

  4. Area = (1/2) * base * cosine(angle)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Aryabhata's formula for calculating the area of a triangle using sine is: Area = (1/2) * base * sine(angle).

Multiple choice

What is the name of the theorem that states that the area of a triangle is equal to half the product of its base and height?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Heron's Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heron's Formula provides a method for calculating the area of a triangle using its side lengths.

Multiple choice

The Pythagorean Theorem can be used to find the area of a right triangle. True or False?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem can be used to find the area of a right triangle. The area of a right triangle is given by the formula: (A = \frac{1}{2}ab), where (a) and (b) are the lengths of the two legs of the triangle. This formula is derived using the Pythagorean Theorem.

Multiple choice

Determine the area of a triangle with base 10 cm and height 8 cm.

  1. 40 cm²

  2. 80 cm²

  3. 20 cm²

  4. 160 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of a triangle = (1/2) * base * height = (1/2) * 10 cm * 8 cm = 40 cm²

Multiple choice

What is the formula for calculating the area of a triangle?

  1. A = 1/2 * b * h

  2. A = b * h

  3. A = 1/2 * b^2

  4. A = b^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the area of a triangle is A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle.

Multiple choice

In the 2020 China Girls' Mathematical Olympiad, what was the area of a triangle with sides of length 6 cm, 8 cm, and 10 cm?

  1. 24 cm^2

  2. 30 cm^2

  3. 36 cm^2

  4. 42 cm^2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the area of a triangle with sides of length a, b, and c, we can use Heron's formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle. In this case, s = (6 + 8 + 10) / 2 = 12. Plugging in the values a = 6, b = 8, and c = 10, we get Area = √(12(12-6)(12-8)(12-10)) = √(12 * 6 * 4 * 2) = 36 cm^2.

Multiple choice

In the 2008 China Girls' Mathematical Olympiad, what was the area of a triangle with base 12 cm and height 8 cm?

  1. 48 cm^2

  2. 64 cm^2

  3. 80 cm^2

  4. 96 cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a triangle with base b and height h is given by the formula A = (1/2)bh. Plugging in the values b = 12 and h = 8, we get A = (1/2)(12)(8) = 48 cm^2.

Multiple choice

Find the perimeter of a triangle with sides of length 6 cm, 8 cm, and 10 cm.

  1. 24 cm

  2. 26 cm

  3. 28 cm

  4. 30 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of the given triangle is: $$Perimeter = 6 cm + 8 cm + 10 cm$$ $$Perimeter = 24 cm$$