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Yes. For example, one triangle could have a base of 4 units, and a height of 1 unit, which means it would have an area of 2 square units. A different triangle could have a base of 2 units, and a height of 2 units, meaning it would also have an area of 2 square units.

Q: Can triangles of different size and shape have the same area?

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If another triangle has the same three sides, that is, sides of the same length, it will have the same area. Note that this is a sufficient, but not a necessary, condition, since you can also have triangles of a different shape that have the same area.

Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.

There are an infinite number of triangles with different shapes that all have the same area.

they are different because perimeter is the out side of the shape and area is inside of the shape.

Three sided polygons would be triangles. Triangles that have the same shape (same angle measures) but are different sizes (different side lengths) would be called similar triangles. In similar triangles, corresponding sides have lengths in the same ratio. If triangle ABC is similar to triangle DEF, then: AB/DE = BC/EF = AC/DF.

Related questions

If another triangle has the same three sides, that is, sides of the same length, it will have the same area. Note that this is a sufficient, but not a necessary, condition, since you can also have triangles of a different shape that have the same area.

Those would be SIMILAR triangles.

Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.

There are an infinite number of triangles with different shapes that all have the same area.

Similar triangles

they are different because perimeter is the out side of the shape and area is inside of the shape.

Three sided polygons would be triangles. Triangles that have the same shape (same angle measures) but are different sizes (different side lengths) would be called similar triangles. In similar triangles, corresponding sides have lengths in the same ratio. If triangle ABC is similar to triangle DEF, then: AB/DE = BC/EF = AC/DF.

congruent triangles

Triangles are similar if they have the same shape (can be different sizes). As long as they are the same shape, one can be rotated or bigger than the other.

Similar triangles are those which have the same set of 3 angles but the length of their sides is perhaps different - in other words they are exactly the same SHAPE but they are different size. Equilateral triangles have all 3 angles equal ( all 60degrees) so the answer is YES.

No, because if they have different heights the area will differ between the two triangles.

No. For example the triangles with sides {3, 4, 5} and {6, 8, 10} are similar but not congruent.