Similar Triangles — Area Ratio Equals Square of Similarity Ratio
Similar Triangles — Area Ratio Equals Square of Similarity Ratio. Practice questions to deepen understanding of the ratio of areas in similar triangles being equal to the square of the similarity ratio. Online math practice with full solutions and step-by-step explanations.
Area ratio in similar triangles practice — ratio of areas = square of the similarity ratio. Comprehensive practice with explanations and proofs.
📐 theorem area:
similar triangles ratio of areas :
:
two similar triangles, similarity ratio side small side large/greater k, ratio of areas small large/greater k square.
altitude :
, side . k. :
- side k.
- altitude k.
- k.
area No two because, double altitude two. Yes k altitude k, area k double k, k square.
ratio of areas similar triangles equal square similarity ratio.
similarity ratio two similar triangles (smaller : larger) 2 3.
ratio of areas smaller : larger?
similarity ratio ratio sides, ratio . area ratio:
- 2 square equal 4.
- 3 square equal 9.
Yes ratio of areas small large/greater 4 9.
ratio of areas two similar triangles (smaller : larger) 9 16.
similarity ratio smaller : larger?
ratio of areas square similarity ratio. Yes similarity ratio calculate square:
- 9 3.
- 16 4.
Yes similarity ratio small large/greater 3 4.
two similar triangles. similarity ratio smaller : larger 3 5.
area small 27 metres .
area larger?
similarity ratio small large/greater 3 5. ratio of areas small large/greater square ratio:
- 3 square 5 square equal 9 25.
:
area small area large/greater equal 9 25.
: area large/greater equal 27 double 25 9 equal 27 double 25 9.
27 9 equal 3, 3 double 25 equal 75.
Yes area large/greater 75 metres .
similarity ratio two similar triangles (smaller : larger) 4 7.
area larger 343 metres .
area small?
similarity ratio small large/greater 4 7. ratio of areas 16 49.
:
area small area large/greater equal 16 49.
area small equal 343 double 16 49.
343 49 equal 7, 7 double 16 equal 112.
Yes area small 112 metres .
similarity ratio two similar triangles 2 5.
because ratio of areas 2 5.
because Yes ?
side area. similarity ratio sides . area altitude two. altitude 2, area 4.
Yes similarity ratio 2 5, ratio of areas 4 25 No 2 5. area side one, because two because .
two similar triangles. one area .
similarity ratio smaller : larger 1 3, ratio of areas smaller : larger?
Explanation: See the definition and relevant formula above.
area small 25 metres , area larger 100 metres .
similarity ratio smaller : larger?
ratio of areas small large/greater 25 100, 1 4.
ratio of areas square similarity ratio. Yes similarity ratio 1 4, 1 2.
smaller : larger . similarity ratio smaller : larger 2 7.
area small 18 metres .
area ?
similarity ratio small large/greater 2 7. ratio of areas 4 49.
: area small area large/greater equal 4 49.
area large/greater equal 18 double 49 4.
18 4 equal 4 half, : 18 double 49 equal 882, 882 4 equal 220 . , :
. No .
Yes given . ratio 220 , No , Yes approx. , 308. .
: " similarity ratio 3 5, ratio perimeters ratio of areas 9 25".
Correct ?
perimeter sides Yes . ratio perimeters equal similarity ratio, 3 5. , area two , Yes ratio of areas square similarity ratio, 9 25.
two similar triangles. small area 10, larger No .
similarity ratio smaller : larger 1 4, area larger?
Explanation: See the definition and relevant formula above.
sides corresponding two similar triangles find ratio 5 6 (smaller : larger).
ratio of areas smaller : larger?
ratio sides small large/greater 5 6. ratio of areas square ratio sides:
- 5 square equal 25.
- 6 square equal 36.
Yes ratio of areas small large/greater 25 36.
area one 18 metres , area 50 metres .
similar triangles?
ratio of areas ratio square . similar triangles ratio . theorem ratio of areas square similarity ratio, .
ratio of areas two similar triangles 9 25 (smaller : larger).
ratio perimeters smaller : larger?
ratio of areas square similarity ratio. Yes similarity ratio small large/greater 3 5.
perimeter Yes ratio perimeters equal similarity ratio, 3 5.
two similar triangles. area small 20 metres , area larger 80 metres .
side small 5 metres.
side larger?
ratio of areas small large/greater 20 80, 1 4. Yes similarity ratio small large/greater 1 2.
side small 5, side large/greater 5 double 2 equal 10.
two square . side square small 2 metres, side square larger 5 metres.
ratio of areas smaller : larger?
ratio sides small large/greater 2 5. area square square side, Yes ratio of areas 4 25. similar triangles .
ratio of areas two similar triangles 1 49 (smaller : larger).
similarity ratio smaller : larger?
area ratio 1 49. similarity ratio ratio of areas:
- 1 1.
- 49 7.
Yes similarity ratio small large/greater 1 7.
ratio of areas two similar triangles 16 25 (smaller : larger).
similarity ratio smaller : larger 4 25.
Yes ?
ratio of areas ratio , square . No .
16 25 4 5, No 4 25.
two similar triangles. similarity ratio smaller : larger 3 8.
ratio of areas smaller : larger?
theorem :
- square 3 9.
- square 8 64.
Yes ratio of areas small large/greater 9 64. , .
two similar triangles , one two.
ratio sides smaller : larger 1 2, larger area larger area small?
Explanation: See the definition and relevant formula above.
, small 1 50 ( ). area 6 metres .
area ?
1 50 large/greater 50 . ratio of areas square similarity ratio:
- 1 2500.
area 6, area 6 double 2500 equal 15000.
similarity ratio two similar triangles 5 3 (smaller : larger). one because ratio of areas smaller : larger 10 6.
ratio of areas Correct?
similarity ratio 5 3. ratio of areas 25 9. ratio 10 6 5 3, ratio No ratio of areas. Yes ratio of areas 10 6 Correct.
one area 12 metres area 27 metres . two similar triangles, similarity ratio smaller : larger?
ratio of areas small large/greater 12 27, 4 9. similarity ratio 4 9, 2 3.
Yes Yes , similarity ratio small large/greater 2 3.
square similarity ratio theorem area similar triangles?
area double altitude two. k, altitude k. Yes area k double k, k square.
ratio of areas similar triangles square similarity ratio.
theorem theorem area similar triangles:
theorem , sides ratio, area by/according to ratio No by/according to square ratio. area two : altitude.
one theorem , , .