Advertisements
Advertisements
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.
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
APPEARS IN
RELATED QUESTIONS
A point D is taken on the side BC of a ΔABC such that BD = 2DC. Prove that ar(Δ ABD) =
2ar (ΔADC).
In the below fig. X and Y are the mid-points of AC and AB respectively, QP || BC and
CYQ and BXP are straight lines. Prove that ar (Δ ABP) = ar (ΔACQ).
In the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
Diagonal AC and BD of trapezium ABCD, in which AB || DC, intersect each other at O. The triangle which is equal in area of ΔAOD is
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
The side of a square field is 16 m. What will be increase in its area, if each of its sides is increased by 4 m?
This stamp has an area of 4 square cm. Guess how many such stamps will cover this big rectangle.
The region given in the following figure is measured by taking 
as a unit. What is the area of the region?
A magazine charges Rs 300 per 10 sq cm area for advertising. A company decided to order a half page advertisment. If each page of the magazine is 15 cm × 24 cm, what amount will the company has to pay for it?
How will you decide? Discuss.
