Question

In the figure , PQRS is a square. U and V are midpoints of QR and RS respectively.
The area of the square TURV is 36 sq cm. What is the area PQUT?

Answer 1

The answer is 54 sq. cm

Step-by-step explanation:

PQRS is a square, U and V are the midpoints of side QR and RS, and the area of square TURV is $36 cm^2.$

Hence, point P is located at the center of the square.

Now, to find the area of PQUT, we need to find the area of square TUQW and triangle PTW and add them ( See attachment for the figure)

Since the area of square TURV is $36 cm^2,$ it means each side has a length of 6 cm.

Area of square TUQW $= side^2 = 6^2 = 36 cm^2$

Area of triangle PTW

$= \frac{1}{2} \times base\times altitude$

$= \frac{1}{2} \times 6 \times 6$

$= 18 cm^2$

Hence area of PQUT$= 36 + 18 = 54 cm^2$