Question

If the area of ABC is 20 cm2, what is the area of PQR? Show your work.

Answer 1

Area of ΔPQR = 45 cm²

Explanation:

From the given figure we can see that triangle ABC and triangle PQR are similar triangles.

If two triangles are similar the the ratio of area of two triangle is equal to the square of ratio of corresponding sides

To find the area of triangle PQR

Ar(ABC) = 20, AB = 4 cm and PQ =6 cm

From figure we can write,

Ar(ABC)/ar(PQR) = (AB/PQ)²

20/ar(PQR) = (4/6)²

20/ar(PQR) = 16/36

ar(PQR) = (36 x 20)/16 = 45 cm²

Answer 2

Since the triangles are similar, the first thing to do is find the scale factor.
We have then:
k = 6/4 = 3/2
Then, the area will be given by:
A '= k ^ 2 * A
Substituting values:
A '= ((3/2) ^ 2) * (20)
A '= 45 cm ^ 2
Answer:
The area of PQR is:
A '= 45 cm ^ 2