given that triangle PQR is similar to triangle STU and that corresponding sides PQ=4cm and ST=6cm. The area of STU is 12cm squared. state the area of PQR

the linear scale factor is 4:6 or 2:3

so the area scale factor is 4:9
4/9 of 12 cm^2 is 16/3 cm^2

To find the area of triangle PQR, we need to know the ratio between the lengths of the corresponding sides of triangles PQR and STU.

Since triangle PQR is similar to triangle STU, the ratio of corresponding side lengths is the same. In this case, we have PQ/ST = 4/6 = 2/3.

Now, we can use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Let's calculate the area of PQR using this information:

(area of PQR)/(area of STU) = (PQ/ST)^2
(area of PQR)/12 = (2/3)^2
(area of PQR)/12 = 4/9

To find the area of PQR, we can solve for it by cross-multiplying:

(area of PQR) = 12 * (4/9) = 48/9 = 5.33 (rounded to two decimal places).

Therefore, the area of triangle PQR is approximately 5.33 square cm.

To find the area of triangle PQR, we can use the concept of similarity.

Since triangle PQR is similar to triangle STU, the ratio of their corresponding sides is proportional. We can set up the proportion:

PQ/ST = QR/TU

Substituting the given values, we have:

4/6 = QR/TU

Simplifying the proportion:

2/3 = QR/TU

Now, let's find the ratio of the areas of the two triangles PQR and STU. The area of a triangle is proportional to the square of its corresponding sides.

(PQ/ST)^2 = (area of PQR/area of STU)

(4/6)^2 = (area of PQR/12)

16/36 = (area of PQR/12)

Dividing both sides by 36:

16/36 * 12 = area of PQR

4/9 * 12 = area of PQR

48/9 = area of PQR

The area of triangle PQR is 48/9 cm² or 16/3 cm².