Calculating the Areas and Perimeters of Triangles
Area of a triangle: A = (1/2)bh
b is the base of the triangle
h is the height of the triangle
Area of an equilateral triangle: A = (sqrt(3)/4)s²
Perimeter of a triangle: P = a + b + c
perimeter of an equilateral triangle: P = 3 x side length
Question 1:
Find the area of a triangle with base 6 cm and height 8 cm.
Solution:
A = (1/2)bh
A= (1/2)(6 cm)(8 cm) = 24 cm².
Requested by: Zaib
Question 2:
Find the perimeter of a triangle with sides of length 3 cm, 4 cm, and 5 cm.
Solution:
P = a + b + c
P = 3 cm + 4 cm + 5 cm = 12 cm.
Requested by: Zaib
Question 3:
Find the perimeter of a triangle with sides of length 12 cm, 15 cm, and 18 cm.
Solution:
P = a + b + c =
P = 12 cm + 15 cm + 18 cm = 45 cm.
Requested by: Ameer
Question 4:
Find the area of an equilateral triangle with side length 10 cm.
Solution:
A = (sqrt(3)/4)s²
A = (sqrt(3)/4)(10 cm)² = 25(sqrt(3)) cm².
Requested by: Saroop
Question 5:
Find the perimeter of an isosceles triangle with sides of length 6 cm, 6 cm, and 8 cm.
Solution:
P = a + b + c
P= 6 cm + 6 cm + 8 cm = 20 cm.
Requested by: Naeem
Question 6:
Find the area of an isosceles triangle with base 8 cm and height 6 cm.
Solution:
Area = (1/2) x base x height
Area = (1/2) x 8 cm x 6 cm
Area = 24 cm²
Requested by: Naeem
Question 7:
Find the perimeter of a right triangle with hypotenuse 10 cm and one leg of length 6 cm.
Solution:
Let the other leg of the triangle be x cm.
Using Pythagorean theorem, we have:
x² + 6² = 10²
x² + 36 = 100
x² = 64
x = 8 cm
Therefore, the perimeter of the triangle is:
Perimeter = 6 cm + 8 cm + 10 cm
Perimeter = 24 cm
Requested by: Kantesh
Question 8:
Find the area of a triangle with a base of 10 cm and a height of 6 cm.
Solution:
Area = (1/2)bh = (1/2) * 10 cm * 6 cm = 30 cm^2
Requested by: Ali Raza
Question 9:
Find the area of a triangle with side lengths of 6 cm, 8 cm, and 10 cm.
Solution:
This is a special triangle known as a “right triangle”, since one of its angles measures 90 degrees.
We can use the formula for the area of a triangle and the Pythagorean theorem to find its height:
Area = (1/2)bh
b = 6 cm (the length of the base)
c = 10 cm (the length of the hypotenuse)
a = sqrt(c^2 – b^2) = sqrt(10^2 – 6^2) = 8 cm (the length of the height)
Therefore, the area of the triangle is:
Area = (1/2)bh = (1/2) * 6 cm * 8 cm = 24 cm^2
Requested by: Saramd
Question 10:
Find the perimeter of a triangle with side lengths of 7 cm, 8 cm, and 9 cm.
Solution:
Perimeter = sum of all sides = 7 cm + 8 cm + 9 cm = 24 cm
Requested by: Sarmad
Question 11:
Find the perimeter of an isosceles triangle with base length 6 cm and height 8 cm.
Solution:
Since this is an isosceles triangle, we know that the two other sides are equal.
Let’s call their length x.
Using the Pythagorean theorem, we can find x:
x^2 = 8^2 + (1/2 * 6)^2 = 64 + 9 = 73
x = sqrt(73) ≈ 8.5 cm
The perimeter of the triangle is:
Perimeter = base + 2 equal sides = 6 cm + 2(8.5 cm) = 23 cm.
Requested by: Sarmad
Question 12:
Find the perimeter of a triangle with sides of length 6 cm, 8 cm, and 10 cm.
Solution:
Perimeter = 6 cm + 8 cm + 10 cm
Perimeter = 24 cm
Requested by: Hallar
Question 13:
Find the area of a right triangle with legs of length 3 cm and 4 cm.
Solution:
Area = (1/2) x base x height
Area = (1/2) x 3 cm x 4 cm
Area = 6 cm²
Requested by: Sarmad
Question 14:
Find the perimeter of an equilateral triangle with sides of length 5 cm.
Solution:
Perimeter = 3 x side length
Perimeter = 3 x 5 cm
Perimeter = 15 cm
Requested by: Sarmad
Question 15:
Find the perimeter of a right triangle with legs of length 5 cm and 12 cm.
Solution:
Using Pythagorean theorem, we have:
hypotenuse = sqrt(5² + 12²) = 13 cm
Perimeter = 5 cm + 12 cm + 13 cm
Perimeter = 30 cm
Requested by: Kabeer
Question 16:
Find the area of a triangle with sides of length 3 cm, 4 cm, and 5 cm.
Solution:
This is a right triangle, so we can use the formula for the area of a right triangle:
Area = (1/2) x base x height
Area = (1/2) x 3 cm x 4 cm
Area = 6 cm²
Requested by: Kabeer
Question 17:
Find the perimeter of a triangle with sides of length 12 cm, 16 cm, and 20 cm.
Solution:
Perimeter = 12 cm + 16 cm + 20 cm
Perimeter = 48 cm
Requested by: Faizan
Question 18:
Find the perimeter of a triangle with sides of length 9 cm, 12 cm, and 15 cm.
Solution: P = a + b + c = 9 cm + 12 cm + 15 cm = 36 cm.
Requested by: Faizan
Question 19:
Find the area of an equilateral triangle with side length 8 cm.
Solution: An equilateral triangle has all sides equal, so the height can be found using the Pythagorean theorem:
h = sqrt(8 cm² – (4 cm²)) = sqrt(48) cm = 4sqrt(3) cm.
Therefore, A = (1/2)bh = (1/2)(8 cm)(4sqrt(3) cm)
A = 16sqrt(3) cm².
Requested by: Faizan
Question 20:
Find the area of a right triangle with legs of length 3 cm and 4 cm.
Solution: A = (1/2)bh = (1/2)(3 cm)(4 cm) = 6 cm².
Requested by: Hamid
Question 21:
Find the perimeter of a right triangle with legs of length 5 cm and 12 cm.
Solution:
The hypotenuse can be found using the Pythagorean theorem:
c = sqrt(5 cm² + 12 cm²) = 13 cm.
Therefore, P = a + b + c = 5 cm + 12 cm + 13 cm
P = 30 cm.
Requested by: Hamid
Question 22:
Find the area of a triangle with base 12 cm and height 9 cm.
Solution: A = (1/2)bh = (1/2)(12 cm)(9 cm) = 54 cm².
Requested by: Ali Nawaz
Question 23:
Find the perimeter of a triangle with sides of length 8 cm, 10 cm, and 12 cm.
Solution: P = a + b + c = 8 cm + 10 cm + 12 cm = 30 cm.
Requested by: Ali Nawaz
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