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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