Understanding Ratios of Areas in Triangles

If two triangles share the same height, what determines the ratio of their areas?

• The ratio of their heights

• The ratio of their bases

• The sum of their bases

• The difference in their heights

When two triangles share a common base, what determines the ratio of their areas?

• The difference in their bases

• The sum of their heights

• The ratio of their heights

• The ratio of their bases

What is the relationship between the scale factor of similar triangles and the ratio of their areas?

• The ratio of their areas is the cube of the scale factor

• The ratio of their areas is the scale factor

• The ratio of their areas is the inverse of the scale factor

• The ratio of their areas is the square of the scale factor

In a pair of similar triangles, if the scale factor is 3:4, what is the ratio of their areas?

• 3:4

• 9:16

• 6:8

• 12:16

If triangle ABC has a base of 12 and triangle ABD has a base of 9, what is the ratio of their areas if they share the same height?

• 2:1

• 3:4

• 1:2

• 4:3

If the area of two similar triangles is 144 and 169, what is the scale factor between them?

• 1:1

• 12:13

• 13:12

• 2:3

If two triangles have a height ratio of 3:1 and share a common base, what is the ratio of their areas?

• 1:3

• 3:1

• 2:1

• 1:2

In a trapezoid with parallel sides, if the scale factor between two similar triangles is 1:2, what is the ratio of their areas?

• 2:3

• 1:2

• 3:4

• 1:4

In a problem involving a trapezoid, if one triangle has an area ratio of 1:4 with another, what is the scale factor of their sides?

• 1:2

• 1:3

• 2:3

• 3:4

In a trapezoid, if the ratio of the areas of two triangles is 1:9, what is the scale factor of their corresponding sides?

• 1:3

• 9:1

• 1:9

• 3:1