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Question
In square ABCD, P and Q are mid-point of AB and CD respectively. If AB = 8cm and PQand BD intersect at O, then find area of ΔOPB.
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Solution
Given: Here from the given question we get
(1) ABCD is a square,
(2) P is the midpoint of AB
(3) Q is the midpoint of CD
(4) PQ and BD intersect at O.
(5) AB = 8cm
To find : Area of ΔOPB
Calculation: Since P is the midpoint of AB,
`BP = 1/2 (AB) `
= 1/2 (8)`
= 4 cm
BP = 4cm ……(1)
Area of triangle = `1/2 `× base × height
Area of ΔOPB = `1/2` × BP × PO (from 1)
` = 1/2 × 4 × (PO = 1/2 AD , APQD ` is a rectangle)
`= 1/2 × 16 `
Area of ΔOPB = 8 cm2
Hence we get the Area of ΔOBP = 8 cm2
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