# A small triangle has the area of 14cm² . Determine the area of a larger similar triangle which has been enlarged by a scale factor of 4?

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• Anonymous
7 months ago

This is where you have to be careful, your scale factor applies to linear dimensions:

As an example say your triangle has a base of 14 and height of 2 gives area of 14

But your new triangle would be 56 and 8: an area of 224 (not 14 x 4 = 56)

What happens is your square area increases by a factor 4 x 4 ( or 4 squared) = 16

Thus: 14 x 16 = 224 sqcm

The actual dimensions are unimportant if you know the linear factor is 4, the square will be a factor of the square of that, ie 16 (and the volume a factor of 64 ie 4 cubed).

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• A=1/2*4*7=14

A2=1/2*16*28=16*14 = 228cm^2

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• Let x and y represent the base and height of the small triangle.

Since the larger triangle is similar with an enlarged scale of 4,

we know that 4x and 4y are the base and height of the large triangle.

The area of the small triangle is given as 14 cm², so

½ xy = 14 cm²

The area of hte large triangle is therefore

½ (4x)(4y) = ½ (4) (xy)

.................= 4 [½ xy]

.................= 4 [14cm²]

.................= 64 cm².............ANS

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• You can use any two numbers that multiply to make 14

What can divide into 14?

7 and 2

7 x 2 = 14

Multiply them by a factor of 4 and you get

28 and 8

8 x 28 = 224 sq cm

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• --

A1 = 14 cm²

A2 = 16 x 14 = 224 cm²

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• A small triangle has the area of 14 cm².

The area of a larger similar triangle

which has been enlarged by a scale factor of 4:

224 cm².

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• Quadruple both sides of a square. What happens to its area? That works for all shapes.

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