Question

Triangles ABC and DEF are mathematically similar.
CB = 9cm
FE = 13.5cm
The area of triangle ABC is 34cm squared
Calculate the area of triangle DEF

Answer 1

Answer:

ABC=DEF (Given)

So, height of ABC= height of DEF

CB=9cm

FE=13.5cm

Area of ABC= 34cm square

As we know the area of a triangle= 1/2 × base × height,

again, area of ABC= 1/2 × base × height= 34cm square

=>1/2 × 9cm × height= 34cm square

=>9/2cm × height= 34cm square

=>height= 34cm square/(9/2cm)

=>height= (34 × 2/9)cm

=>height= (68/9)cm

Now, area of DEF= 1/2 × base × height

= 1/2 × 13.5cm × (68/9)cm

= 1/2 × (135/10)cm × (68/9)cm

= 51cm square

Therefore, the area of triangle DEF is 51cm square.

Answer 2

Answer:

76.5cm^2

Step-by-step explanation:

Side CB = 9cm

Side FE = 13.5cm

Since these are mathematically similar, you can find the scale factor.

13.5cm / 9cm = 1.5

1.5 is the length scale factor

to find the area scale factor do length scale factor ^2

1.5^2 = 2.25

Area (34cm^2) x 2.25 = 76.5cm^2