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Answer:
TRIANGLES
Possible
4) Yes
Unique
1) No
2) No
3) Yes
3D SHAPES
Step 2: triangle area 8.75 ft²; total area 52.5 ft²
Step 3: TOTAL AREA = 52.5 ft² + 31.5 ft² = 84 ft²
Step-by-step explanation:
TRIANGLES
Possible Triangles
The requirement on side lengths is that the sum of the short two exceed the longest.
4) 5 + 6 = 11 > 7 . . . . Yes, can form a triangle
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Unique Triangles
The available congruence theorems are a good starting point for determining if a triangle is unique. If you have side and angle definitions that correspond to AAS, ASA, SAS, SSS, or HL, then the triangle is uniquely determined.
You will notice that SSA is not on this list. However, there are special cases where SSA can be used. If the given angle is opposite the longest given side, then the triangle is uniquely determined. (You will notice that this is the case in an HL triangle, where the given H side is opposite the right angle.)
1) SSA; angle is opposite the short side — triangle is not unique
2) AAA; no side is given — triangle is not unique
3) SAS; — triangle is unique
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3D SHAPES
Step 2: The area is 1/2bh = 1/2(3.5 ft)(5 ft) = 8.75 ft². The area of all triangles together is 6×8.75 ft² = 52.5 ft².
Step 3: TOTAL AREA = 52.5 ft² + 31.5 ft² = 84 ft².
