If ST is parallel to QR, and PS = SQ = 3 cm, PT = 4 cm and QR = 10 cm, what is the area of trapezoid STQR?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 18
Answer is option (e). Triangle PST & PQR are similar.

Thus, $\frac{P S}{P Q} = \frac{P T}{P R}$ ; PR=8

Thus, PQR is a right angled triangle with sides-6,8,10

Area of trapezoid STQR = Area of triangle PQR- Area of triangle PST = $\frac{1}{2}$ $\times$ 6 $\times$ 8 - $\frac{1}{2}$ $\times$ 3 $\times$ 4. Answer is 18 cm $^{2}$

Suggest Corrections

Similar questions

Q. In the figure,

P S = 4 c m, S R = 2 c m, P T = 3 c m

and

Q T = 5 c m

.
Calculate

S T

, if

Q R = 5.8 c m

Q. In a triangle PQR, ST is parallel to QR Show that RT(PQ + PS) = SQ (PR + PT)

Q. In

△ P Q R, S T ∥ Q R

and

\frac{P S}{S Q} = \frac{3}{5}

P R = 6

cm find

P T

In the figure below, if the line segment ST is parallel to line segment QR such that $\frac{P S}{S Q} = \frac{P T}{T R}$ . This provided data is not sufficient to prove that
$\frac{S T}{Q R} = \frac{P T}{T R}$

Q. In the adjoining figure (not drawn to scale),

P S = 4 c m, S R = 2 c m, P T = 3 c m

and

Q T = 5 c m

,
(i) Show that

△ P Q R \sim △ P S T

.
(ii) Calculate

S T

, if

Q R = 5 \cdot 8 c m

Join BYJU'S Learning Program

If ST is parallel to QR, and PS = SQ = 3 cm, PT = 4 cm and QR = 10 cm, what is the area of trapezoid STQR?

The correct option is D 18Answer is option (e). Triangle PST & PQR are similar. Thus, PSPQ=PTPR; PR=8 Thus, PQR is a right angled triangle with sides-6,8,10 Area of trapezoid STQR = Area of triangle PQR- Area of triangle PST = 12×6×8 - 12× 3× 4. Answer is 18 cm2