Question

part b
if db = 85 feet and ac = 28 feet, what is the combined area of the two triangles in the diagram?
statements
1.?
2.?
3.?
4.?
reasons
given
def. of angle bisector
reflexive property
asa
① keyboard help
\\(\overline{ac}\\) bisects \\(\angle dcb\\) and \\(\angle dac \cong \angle bac\\)
\\(\angle dca \cong \angle bca\\)
\\(\overline{ac} \cong \overline{ac}\\)
\\(\triangle dac \cong \triangle bac\\)

Explanation:

Step1: Identify Triangle Congruence

From the proof, \(\triangle DAC \cong \triangle BAC\) (ASA congruence). So their areas are equal.

Step2: Determine the Base and Height for Area

The combined area of the two triangles is the area of \(\triangle DAB\), where \(DB\) is the base and \(AC\) is the height (since \(AC\) is perpendicular? Assuming from the diagram context, as \(AC\) bisects angles and triangles are congruent, \(AC\) is the height relative to base \(DB\)).

Step3: Calculate Area of \(\triangle DAB\)

The formula for the area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\). Here, base \(DB = 85\) feet, height \(AC = 28\) feet.
So area \(= \frac{1}{2} \times 85 \times 28\)
First, calculate \(85 \times 28 = 2380\)
Then, \(\frac{1}{2} \times 2380 = 1190\) square feet.

Answer:

The combined area of the two triangles is \(\boxed{1190}\) square feet.