Question

finding the area of a triangle
what information relevant to calculating area do we have available for this
triangle?
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 known side lengths

We have all 3 sides: $a=7$, $b=10$, $c=12$

Step2: Calculate semi-perimeter $s$

$$s=\frac{a+b+c}{2}=\frac{7+10+12}{2}=\frac{29}{2}=14.5$$

Step3: Apply Heron's formula

Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$$=\sqrt{14.5(14.5-7)(14.5-10)(14.5-12)}$$
$$=\sqrt{14.5\times7.5\times4.5\times2.5}$$
$$=\sqrt{14.5\times84.375}$$
$$=\sqrt{1223.4375}$$

Step4: Compute final value (round to 2 decimals)

$\sqrt{1223.4375}\approx34.98$

Answer:

What information relevant to calculating area do we have available for this triangle?

All three side lengths (7, 10, 12)

Which method should we use to calculate the area for this triangle?

Heron's Formula

What is the area of this triangle calculated to the nearest hundredth of a square unit?

34.98