In the rectangle P
Q
R
S
, the side
P
Q
is of length
2
and the side
Q
R
is of length
4
.

Points
T
and
U
lie inside the rectangle so that
P
Q
T
and
R
S
U
are equilateral triangles.

What is the area of the quadrilateral
Q
R
U
T
?

In order to form triangle PQT and quadrilateral TQRS, point T must lie on line PS which is 16 cm. long.

If the ratio of PT to TS is 5:3 and the total length of PS is 16, then PT must be 10 and TS must be 6 (10 + 6 =16) and 10:6 is the same ratio as 5:3. Another way to think about it is 5/3 = 10/6.

Now you have all the lengths that you need to find the areas of the quadrilateral and the triangle.

Make sure you draw a diagram of it!!