# PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig. 9.9). Find the area of ∆ OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS.

**Solution:**

Given, PQRS is a square.

T and U are the midpoints of PS and QR

O is the point of intersection of TU and QS

We have to find the area of triangle OTS, if PQ = 8cm.

We know that all the sides of a square are equal in length.

So, PQ = QR = RS = PS

Given, PQ = 8 cm

So, PS = 8 cm

T is the midpoint of PS

So, PT = ST = 1/2 PS

ST = 8/2

ST = 4 cm

From the figure,

PQ = TU

So, OT = PQ/2

OT = 8/2

OT = 4 cm

Area of triangle = 1/2 × base × height

Area of triangle OTS = 1/2 × 4 × 4

= 2 × 4

= 8 cm²

Therefore, the area of the triangle OTS is 8 cm².

**✦ Try This:** ABCD is a square. P and Q are, respectively, the mid-points of AB and CD. Find the area of ∆ OPD, if AB = 10 cm, where O is the point of intersection of PQ and BD.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 9

**NCERT Exemplar Class 9 Maths Exercise 9.3 Sample Problem 1**

## PQRS is a square. T and U are respectively, the mid-points of PS and QR (Fig. 9.9). Find the area of ∆ OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS.

**Summary:**

PQRS is a square. T and U are the mid-points of PS and QR (Fig. 9.9). The area of ∆ OTS, if PQ = 8 cm, where O is the point of intersection of TU and QS is 8 cm²

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