Find the area of a non-right triangle if the side lengths are 122 m, 22 m and 120 m respectively.

Question 21 options:

1420 sq.m

1300 sq.m

1400 sq.m

1320 sq.m

1 answer

To find the area of a non-right triangle with given side lengths, we can use Heron's formula. Heron's formula states that the area \( A \) of a triangle with sides of lengths \( a \), \( b \), and \( c \) is given by:

\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]

where \( s \) is the semi-perimeter of the triangle, calculated as:

\[ s = \frac{a + b + c}{2} \]

For the side lengths \( a = 122 \) m, \( b = 22 \) m, and \( c = 120 \) m, we first calculate the semi-perimeter \( s \):

\[ s = \frac{122 + 22 + 120}{2} = \frac{264}{2} = 132 \text{ m} \]

Next, we find \( s - a \), \( s - b \), and \( s - c \):

\[ s - a = 132 - 122 = 10 \text{ m} \] \[ s - b = 132 - 22 = 110 \text{ m} \] \[ s - c = 132 - 120 = 12 \text{ m} \]

Now, we can use these values in Heron's formula:

\[ A = \sqrt{132 \cdot 10 \cdot 110 \cdot 12} \]

We calculate the product inside the square root:

\[ 132 \cdot 10 = 1320 \] \[ 1320 \cdot 110 = 145200 \] \[ 145200 \cdot 12 = 1742400 \]

Now we take the square root:

\[ A = \sqrt{1742400} \]

Calculating the square root:

\[ A \approx 1316.5 \text{ sq.m} \]

Rounding this to the nearest option given in the problem, the closest area is:

\[ \text{Area} \approx 1320 \text{ sq.m} \]

Thus, the area of the triangle is approximately:

\(\boxed{1320 \text{ sq.m}}\)