Question

finding the area of a triangle
what information relevant to calculating area do we have available for this triangle?
sss
which method should we use to calculate the area for this triangle?
what is the area of this triangle calculated to the nearest hundredth of a square unit?

Explanation:

Step1: Identify the sides

The triangle has sides \( a = 7 \), \( b = 10 \), \( c = 12 \).

Step2: Calculate the semi - perimeter (\( s \))

The formula for semi - perimeter is \( s=\frac{a + b + c}{2}\).
Substitute the values: \( s=\frac{7+10 + 12}{2}=\frac{29}{2}=14.5 \)

Step3: Apply Heron's formula

Heron's formula for the area (\( A \)) of a triangle with sides \( a \), \( b \), \( c \) and semi - perimeter \( s \) is \( A=\sqrt{s(s - a)(s - b)(s - c)} \)
Substitute \( s = 14.5 \), \( a = 7 \), \( b = 10 \), \( c = 12 \)
\( A=\sqrt{14.5\times(14.5 - 7)\times(14.5 - 10)\times(14.5 - 12)} \)
\(=\sqrt{14.5\times7.5\times4.5\times2.5} \)
First, calculate \( 14.5\times7.5 = 108.75 \), \( 4.5\times2.5=11.25 \)
Then, \( 108.75\times11.25 = 1223.4375 \)
\( A=\sqrt{1223.4375}\approx34.98 \)

Answer:

The area of the triangle is approximately \( 34.98 \) square units.