Advertisements
Advertisements
प्रश्न
If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram
Advertisements
उत्तर
Let ΔAPB and parallelogram ABCD lie on base AB and between parallels AB and PC.
To show area ΔAPB = `1/2` Area (ABCD)
Now, draw BQ || AP.
Then ABQP is a parallelogram.
Now area ABQP = Area ABCD .....(They are on same base AB and between same parallels AB and PC)
⇒ ΔPAB ≅ ΔBQP
Area PAB = Area BQP
= `1/2` Area ABQP
= `1/2` Area ABCD
APPEARS IN
संबंधित प्रश्न
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.
Construct ☐ PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ☐ PQRS is a parallelogram, which of the given information is unnecessary?
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between b and c
Which of the following is a property of a parallelogram?
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
