It is given that in a given triangle two sides are 18cm and 10cm and the perimeter is 42cm. We have found its area equal to 21√11 cm2.
☛ Related Questions:
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m (see Fig. 12.9). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
To find the area of a triangle when you know two sides and the perimeter, you can use Heron's formula. Heron's formula is given by:
Area = √[s(s - a)(s - b)(s - c)]
Where:
- "a," "b," and "c" are the lengths of the three sides of the triangle.
- "s" is the semi-perimeter of the triangle, calculated as s = (a + b + c) / 2.
In this case, you're given two sides of the triangle, which are 12 cm and 10 cm, and the perimeter is 42 cm. To find the area, first calculate the semi-perimeter "s" using the given perimeter:
s = (12 cm + 10 cm + c) / 2
42 cm = (22 cm + c) / 2
Now, solve for "c" (the length of the third side):
42 cm * 2 = 22 cm + c
84 cm = 22 cm + c
Subtract 22 cm from both sides:
c = 84 cm - 22 cm
c = 62 cm
Now that you have the lengths of all three sides of the triangle, you can use Heron's formula to find the area:
s = (12 cm + 10 cm + 62 cm) / 2
s = 84 cm / 2
s = 42 cm
Now, plug the values of "a," "b," and "c" into Heron's formula:
Area = √[42(42 - 12)(42 - 10)(42 - 62)]
Area = √[42 * 30 * 32 * (-20)]
Since the square root of a negative number is not a real number (in this context), it means that a triangle with sides 12 cm, 10 cm, and 62 cm cannot exist in Euclidean geometry. Real triangles must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In this case, the sum of the two given sides (12 cm and 10 cm) is less than the length of the third side (62 cm), violating the triangle inequality theorem.
Therefore, there is no valid triangle with the given side lengths, and hence, you cannot calculate its area using Heron's formula.
Answers & Comments
Step-by-step explanation:
Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm
The sides of triangle given: a =18 cm, b = 10 cm
Perimeter of the triangle = (a + b + c)
42 = 18 + 10 + c
42 = 28 + c
c = 42 - 28
c = 14 cm
Semi Perimeter
s = (a + b + c) = 42/2 = 21 cm
By using Heron’s formula,
Area of a triangle = √s(s - a)(s - b)(s - c)
= √21(21 - 18)(21 - 10)(21 - 14)
= √21 × 3 × 11 × 7
= 21√11 cm2
Area of the triangle = 21√11 cm2.
☛ Check: Class 9 Maths NCERT Solutions Chapter 12
Video Solution:
Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 4
Summary:
It is given that in a given triangle two sides are 18cm and 10cm and the perimeter is 42cm. We have found its area equal to 21√11 cm2.
☛ Related Questions:
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m (see Fig. 12.9). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Math worksheets and
Answer:
To find the area of a triangle when you know two sides and the perimeter, you can use Heron's formula. Heron's formula is given by:
Area = √[s(s - a)(s - b)(s - c)]
Where:
- "a," "b," and "c" are the lengths of the three sides of the triangle.
- "s" is the semi-perimeter of the triangle, calculated as s = (a + b + c) / 2.
In this case, you're given two sides of the triangle, which are 12 cm and 10 cm, and the perimeter is 42 cm. To find the area, first calculate the semi-perimeter "s" using the given perimeter:
s = (12 cm + 10 cm + c) / 2
42 cm = (22 cm + c) / 2
Now, solve for "c" (the length of the third side):
42 cm * 2 = 22 cm + c
84 cm = 22 cm + c
Subtract 22 cm from both sides:
c = 84 cm - 22 cm
c = 62 cm
Now that you have the lengths of all three sides of the triangle, you can use Heron's formula to find the area:
s = (12 cm + 10 cm + 62 cm) / 2
s = 84 cm / 2
s = 42 cm
Now, plug the values of "a," "b," and "c" into Heron's formula:
Area = √[42(42 - 12)(42 - 10)(42 - 62)]
Area = √[42 * 30 * 32 * (-20)]
Since the square root of a negative number is not a real number (in this context), it means that a triangle with sides 12 cm, 10 cm, and 62 cm cannot exist in Euclidean geometry. Real triangles must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In this case, the sum of the two given sides (12 cm and 10 cm) is less than the length of the third side (62 cm), violating the triangle inequality theorem.
Therefore, there is no valid triangle with the given side lengths, and hence, you cannot calculate its area using Heron's formula.