Question

the sides of a triangle measure 35 in, 42 in, and 43 in. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth. in² submit

Explanation:

Step1: Use Heron's formula. First, find the semi-perimeter \( s \).

The sides are \( a = 35 \), \( b = 42 \), \( c = 43 \). The formula for semi - perimeter \( s=\frac{a + b + c}{2}\).
So, \( s=\frac{35 + 42+43}{2}=\frac{120}{2} = 60 \).

Step2: Apply Heron's formula for area \( A=\sqrt{s(s - a)(s - b)(s - c)} \).

Substitute \( s = 60 \), \( a = 35 \), \( b = 42 \), \( c = 43 \) into the formula:
\( A=\sqrt{60(60 - 35)(60 - 42)(60 - 43)}=\sqrt{60\times25\times18\times17} \)
First, calculate the product inside the square root: \( 60\times25 = 1500 \), \( 18\times17=306 \), then \( 1500\times306 = 459000 \).
So, \( A=\sqrt{459000}\approx677.5 \) (rounded to the nearest tenth).

Answer:

\( 677.5 \)