Card 1 of 20
EasyStudy card 1
Prompt
State the triangle area formula.
Answer
\(A=\tfrac12bh\).
MathChapter 17: Triangles
Flashcards
Area of a Triangle Flashcards
Twenty cards on base-height selection, equilateral area, perimeter, area ratios, and percent changes.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What relationship must base and height have?
Answer
They must be perpendicular.
Card 3 of 20
EasyStudy card 3
Prompt
May any side be chosen as the base?
Answer
Yes, with the corresponding perpendicular altitude.
Card 4 of 20
EasyStudy card 4
Prompt
State the equilateral-triangle area formula.
Answer
\(A=\frac{\sqrt3}{4}a^2\).
Card 5 of 20
EasyStudy card 5
Prompt
State the triangle perimeter formula.
Answer
\(P=AB+BC+CA\).
Card 6 of 20
EasyStudy card 6
Prompt
Similar side factor is k. What is area factor?
Answer
\(k^2\).
Card 7 of 20
EasyStudy card 7
Prompt
Equal-height triangles have what area ratio?
Answer
Their base ratio.
Card 8 of 20
MediumStudy card 8
Prompt
Equal-base triangles have what area ratio?
Answer
Their height ratio.
Card 9 of 20
MediumStudy card 9
Prompt
Area is 60 and base is 10. Find height.
Answer
12.
Card 10 of 20
MediumStudy card 10
Prompt
Side ratio is 2:5. Find similar-triangle area ratio.
Answer
4:25.
Card 11 of 20
MediumStudy card 11
Prompt
Why can an altitude lie outside a triangle?
Answer
It is perpendicular to the line containing the chosen base, which may require extending that line.
Card 12 of 20
MediumStudy card 12
Prompt
What height does an equilateral side a produce?
Answer
\(a\sqrt3/2\).
Card 13 of 20
MediumStudy card 13
Prompt
Why does an equilateral altitude split the base in half?
Answer
It creates two congruent 30-60-90 halves in an equilateral triangle.
Card 14 of 20
MediumStudy card 14
Prompt
Two equal-height triangles have bases 3 and 7. Area ratio?
Answer
3:7.
Card 15 of 20
MediumStudy card 15
Prompt
Two equal-base triangles have heights 5 and 8. Area ratio?
Answer
5:8.
Card 16 of 20
MediumStudy card 16
Prompt
Base increases 20% and height decreases 25%. Area change?
Answer
Multiply 1.20 by 0.75 = 0.90, so a 10% decrease.
Card 17 of 20
HardStudy card 17
Prompt
What is the common error in similar-triangle area ratios?
Answer
Using the unsquared side ratio.
Card 18 of 20
HardStudy card 18
Prompt
What do square areas on right-triangle sides represent?
Answer
The squared side lengths in \(a^2+b^2=c^2\).
Card 19 of 20
HardStudy card 19
Prompt
How can area and Pythagorean reasoning combine?
Answer
Use area to find a leg or altitude, then Pythagorean to find another side or perimeter.
Card 20 of 20
HardStudy card 20
Prompt
Why should percent changes be multiplied as factors?
Answer
Area contains both base and height, so their independent scale factors multiply.
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