Question

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

Answer 1

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:

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