The statements and reasons for the proof are:
- CN ≅ WN [given]
- ∠C ≅ ∠W [given]
- m∠CNR ≅ ∠WNO [vertical angles theorem]
- ΔCNR ≅ ΔWNO [ASA theorem]
- RN = ON [CPCTC]
<h3>What is the CPCTC and ASA Congruence Theorem?</h3>
When two triangles have two corresponding congruent angles and one corresponding included sides that are congruent, both triangles are congruent by ASA. By implication, the CPCTC states that since they are congruent triangles, all its corresponding parts are congruent to each other.
The statement for the proof along with the reasons in bracket are:
- CN ≅ WN [given]
- ∠C ≅ ∠W [given]
- m∠CNR ≅ ∠WNO [vertical angles theorem]
- ΔCNR ≅ ΔWNO [ASA theorem]
- RN = ON [CPCTC]
Learn more about the CPCTC theorem on:
brainly.com/question/14706064
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Answer:
215.20 ft^2
Step-by-step explanation:
The figure has 2 semi-circles.
First we find the area of each circle using the formula
because that is the area formula for a circle.
The semi-circle to the left gives the diameter which is 22 feet. The radius would be half the diameter thus r=11 for semi-circle one.
Then we are to find the diameter of the second semi-circle. Given the entire length to be 30 feet, 30-22 leaves us with 8 feet as its diameter thus r=4.
Left: r=11
Right: r=4
Then, plugging both into the formula for area of a circle, we get
Left: 380.1327
Right: 50.26548
We must divide each by two because we are only looking for semi-circle which is exactly half the area of a full circle.
Then,
Left: 190.066
Right: 25.1327
190.066+ 25.1327= 215.199 = 215.2ft^2