Question

O
Eco
2. AABC ~ APQR and A(AABC) = 81 cm2. If AB = 6 cm, PQ = 12 cm, find
A(APQR).
o
con
El Orga​

Answer 1

Answer:

∆ABC~∆PQR

ar(∆ABC)/are(∆PQR)=(6/12)²

81/ar(∆PQR)=(1/2)²

81×4=ar(∆PQR

ar(∆PQR)=324cm²

Answer 2

Area (Δ PQR) is 324 cm².

--------------------------------------------------------------------------------------------

Let's understand a few concepts:

To find Area(triangle STU) we must use the Theorem of Areas of Similar Triangles.

What are similar triangles?

Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional to each other.

What is the Theorem of Areas of Similar Triangles?

The theorem states that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

For example: if Δ ABC and ΔPQR are two similar triangles then we can say that,

$\boxed{\bold{\frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \bigg(\frac{AB}{PQ} \bigg)^2 = \bigg(\frac{BC}{QR} \bigg)^2 = \bigg(\frac{AC}{PR} \bigg)^2}}$

 

---------------------------------------------------------------------------------------------

Let's solve the given problem:

Δ ABC ~ Δ PQR

AB = 6 cm

PQ = 12 cm

Area (Δ ABC) = 81 cm²

By using the above theorem of the areas of similar triangles, we get

$\frac{Area (\triangle ABC)}{Area (\triangle PQR)} = \bigg(\frac{AB}{PQ} \bigg)^2$

$\implies \frac{81}{Area (\triangle PQR)} = \bigg(\frac{6}{12} \bigg)^2$  

$\implies \frac{81}{Area (\triangle PQR)} = \bigg(\frac{1}{2} \bigg)^2$  

$\implies \frac{81}{Area (\triangle PQR)} = \frac{1}{4}$  

$\implies Area (\triangle PQR) = 81 \times 4$  

$\implies \bold{Area (\triangle PQR) = 324\:cm^2}$  

 

Thus, the area of triangle PQR is 324 cm².

----------------------------------------------------------------------------------------

Learn more about this topic from brainly.in:

brainly.in/question/180664

brainly.in/question/28614466