Identifying Figures on the Same Base and Between the Same Parallel Lines

Q. In $△$ABC, $\angle$ABC $={90}^{\circ }$; AD = DC; AB =12 cm, BC = 6.5 cm. Find the area of $△$ADB.

Q.

The part of the plane enclosed by a simple closed figure is called a ___ region.

Q.

The given figure shows a pentagon ABCDE, EG, drawn parallel to DA, meets BA produced at G and CF drawn parallel to DB, meets AB produced at F. The area of $\Delta GDF$ is equal to area of ______ .

1. $\Delta ABD$
2. Quadrilateral GBDE
3. Pentagon ABCDE
4. Quadrilateral AFCD

Q.

Rectangle ABCD and Parallelogram PQRS are between the same parallels.If AB=QR and area parallelogram $PQRS=30c{m}^2$, then area Rectangle ABCD= ___$c{m}^2$

1. 15

2. 30

3. 45

4. 60

Q.

The sides of a triangle are $35cm,54cm$ and $61cm$ respectively. The length of its longest altitude

1. $24\sqrt{5}cm$
2. $10\sqrt{5}cm$
3. $16\sqrt{5}cm$
4. $28cm$

Q.

If a planar region formed by a figure N-shaped is made up of 3 non-overlapping planar regions formed by figures A, J and U, then Area(N) = Area(A) + Area(J) + Area(U).

1. True

2. False

Q.

The amount of region enclosed by a plane closed figure is called its ____________

Q.

Find the area of the quadrilateral ABCD whose vertices are respectively A (1, 1), B (7, –3) C (12, 2) and D (7, 21). [4 MARKS]

Q. In $△$ABC, $\angle$ABC $={90}^{\circ }$; AD = DC; AB =12 cm, BC = 6.5 cm. Find the area of $△$ADB.

Q.

For two figures to be on the same base and between the same parallels, one of the lines must be.

1. Making an obtuse angle to the common base

2. Making an acute angle to the common base

3. Perpendicular to the common base

4. The line containing the common base

Q. Trapezium ABCD and parallelogram EFCD have same base and lie between same parallel

1. True
2. False

Q. Two triangles having the same base and equal areas lie between the same .

1. parallels
2. sides
3. angles

Q.

In the given figure, if the altitude and the base of parallelogram are 12 cm and 6 cm respectively, then the area of triangle BEC is:

1. $16c{m}^2$

2. $26c{m}^2$

3. $36c{m}^2$

4. $46c{m}^2$

Q.

If a planar region formed by a figure N-shaped is made up of 3 non-overlapping planar regions formed by figures A, J and U, then what will be Area(N)?

1. Area(N) = Area(A) + Area(J) + Area(U).

2. 0

3. Area(N) = Area(A) + Area(J)

4. Area(N) = Area(A)+ Area(U).

Q. (i) Identify the set of triangles with equal area from the figure given below:

(ii) What will be the Ar($△$ BDG), if Ar($△$CDG) is 27 sq.cm.

Q. When two figures have a common base and are between 2 parallels, then one parallel must be the line containing .

1. the common base
2. a parallel base
3. uncommon base

Q. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(ΔAOD) = ar(ΔBOC).

Q. A rectangle and a square have the same base and are between the same parallels. The ratio of their areas .

1. 1 : 2
2. 1 : 4
3. 1 : 1
4. 2 : 1

Q.

In the figure, ABCD is a trapezium in which AB || DC and its diagonals AC and BD intersect at O. Then ar(∆AOD) is equal to

1. ar(∆COD)

2. ar(∆AOB)

3. ar(∆AOD)

4. ar(∆BOC)

Q.

Points A(1, 0), B(5, 0), C(7, 6) and D(3, 6) are joined to form a quadrilateral ABCD. Point B(5, 0) is joined with E(5, 6) and A(1, 0) is joined with F(1, 6). Quadrilateral ABEF is completed. BD and AE is joined to intersect at O. Which of the following is correct?

1. Area of triangle ADF = (1/2) × Area of triangle BEC

2. Area of triangle ADF = 1 × Area of triangle BEC

3. Area of triangle ADF = (1/4) × Area of triangle BEC

4. Area of triangle ADF = 2×Area of triangle BEC

Q.

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD show that

ar (EFGH) ar (ABCD)

Q. Let $ABCD$ be a parallelogram of area $124c{m}^2$. If $E$ and $F$ are the mid-points of sides $AB$ and $CD$ respectively, then find the area of parallelogram $AEFD$.

Q.

Points A(1, 0), B(5, 0), C(7, 6) and D(3, 6) are joined to form a quadrilateral ABCD. Point B(5, 0) is joined with E(5, 6); and A(1, 0) is joined with F(1, 6). Quadrilateral ABEF is completed. BD and AE is joined to intersect at O. Which of the following is correct?

1. Area of ABODF = (1/2) × Area of BAOEC

2. Area of ABODF = 1×Area of BAOEC

3. Area of ABODF = (1/4) × Area of BAOEC

4. Area of ABODF = 2 × Area of BAOEC

Q.

ABCD is a parallelogram, EBCF is a rectangle and BCG is a triangle between the same parallel lines. The ratio of area of parallelogram : area of rectangle : area of triangle is

1. 1 : 1 : 2

2. 2 : 2 : 1

3. 1 : 2 : 1

4. 4 : 2 : 1

Q.

Parallelogram ABCD and Rectangle EBCF are between the same parallels. If the area of the parallelogram ABCD is $24c{m}^2$, then the area of the rectangle EBCF is

1. $48c{m}^2$

2. $24c{m}^2$

3. $12c{m}^2$

4. $6c{m}^2$

Q. AR || BC. The number of figures that are formed in the given figure with the same base BC and between the same parallels are _______

1. 4
2. 5
3. 6
4. 7

Q.

Which of the following figures lie on the same base and between the same parallels?

1. Fig 1 and Fig 2

2. Fig 2 and Fig 3

3. Fig 1 and Fig 4

4. Fig 2

Q. ABCD is a parallelogram with sides $AB=12cm$, $BC=10cm$ and diagonal $AC=16cm$. Find the approximate area of the parallelogram.

1. $119.8c{m}^2$
2. $103.7c{m}^2$
3. $15.7c{m}^2$
4. None of these

Q. A triangle and a parallelogram have the same base and same base and same area. If the sides of the triangle are $26$ cm, $28$ cm, and $30$ cm and the parallelogram stands on the base $28$ cm, find the height of the parallelogram.

1. $8$ cm
2. $10$ cm
3. $12$ cm
4. $14$ cm

Q.

Here AB $\parallel$ CD. If the altitude of $△$ACD is 6 cm and CD is 8 cm then the area of $△$BCD is:

1. $14c{m}^2$
2. $24c{m}^2$
3. $34c{m}^2$
4. $44c{m}^2$