$P Q R S$ is a parallelogram with area 40 . If $T$ and $V$ are the midpoints of sides $P S$ and $R S$ respectively, then the area of $P R V T$ is
(A) 10
(B) 12
(C) 15
(D) 16
(E) 18

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-050.jpg?height=323&width=520&top_left_y=1481&top_left_x=1201)
Diagonal $P R$ divides parallelogram $P Q R S$ into two equal areas. That is, the area of $\triangle P R S$ is one half of the area of parallelogram $P Q R S$, or 20.

In $\triangle P R S$, we construct median $R T$.

(A median is a line segment that joins a vertex of a triangle to

the midpoint of its opposite side.)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-227.jpg?height=284&width=488&top_left_y=1712&top_left_x=1469)

Median $R T$ divides $\triangle P R S$ into two equal areas since its base, $P S$, is halved while the height remains the same.

That is, the area of $\triangle T R S$ is one half of the area of $\triangle P R S$, or 10 .

Similarly, we construct median $T V$ in $\triangle T R S$, as shown.

Median $T V$ divides $\triangle T R S$ into two equal areas since its base, $S R$, is halved while the height remains the same.

That is, the area of $\triangle T V S$ is one half of the area of $\triangle T R S$, or 5 . The area of $P R V T$ is equal to the area of $\triangle T V S$ subtracted from the area of $\triangle P R S$, or $20-5=15$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-227.jpg?height=285&width=488&top_left_y=2205&top_left_x=1469)

ANSWER: (C)