In the adjoining figure, show that ABCD is a parallelogram.

Calculate the area of ‖gm ABCD.

In a parallelogram ABCD, it is being given that AB = 10 cm and the altitudes corresponding to the sides AB and AD are DL = 6 cm and BM = 8 cm, respectively. Find AD.

Find the area of a rhombus, the lengths of whose diagonals are 16 cm and 24 cm respectively.

Find the area of a trapezium whose parallel sides are 9 cm and 6 cm respectively and the distance between these sides is 8 cm.

Calculate the area of quad. ABCD, given in Fig. (i).

Calculate the area of trap. PQRS, given in Fig. (ii).

In the adjoining figure, ABCD is a trapezium in which AB ‖ DC; AB = 7 cm; AD = BC = 5 cm and the distance between AB and DC is 4 cm. Find the length of DC and hence, find the area of trap. ABCD.

BD is one of the diagonals of a quad. ABCD. If AL ⊥ BD and CM ⊥ BD, show that ar(quad. ABCD) = x BD x (AL + CM).

In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 14 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.

In the adjoining figure, ABCD is a trapezium in which AB ‖ DC and its diagonals AC and BD intersect at O. Prove that ar(∆AOD) = ar(∆BOC).

In the adjoining figure, DE ‖ BC. Prove that

(i) ar(∆ACD) = ar(∆ABE),

(ii) ar(∆OCE) = ar(∆OBD).

In the adjoining figure, D and E are points on the sides AB and AC of ∆ABC such that ar(∆BCE) = ar(∆BCD).

Show that DE ‖ BC.

In the adjoining figure, O is any point inside a parallelogram ABCD. Prove that

(i) ar(∆OAB) + ar(∆OCD) = ar(‖gm ABCD),

(ii)ar(∆OAD) + ar(∆OBC) = ar(‖gm ABCD).

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P.

Prove that ar(∆ABP) = (quad.ABCD).

In the adjoining figure, ∆ABC and ∆DBC are on the same base BC with A and D on opposite sides of BC such that ar(∆ABC) = ar(∆DBC).

Show that BC bisects AD.

In the adjoining figure, AD is one of the medians of a ∆ABC and P is a point on AD.

Prove that

(i) ar(∆BDP) = ar(∆CDP)

(ii) ar(∆ABP) = ar(∆ACP)

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O.

If BO = OD, prove that

Ar(∆ABC) = ar(∆ADC).

ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Prove that ar(∆BED) = ar(∆ABC).

The vertex A of ∆ABC is joined to a point D on the side BC. The midpoint of AD is E. Prove that ar(∆BEC) = ar(∆ABC).

D is the midpoint of side BC of ∆ABC and E is the midpoint of BD. If O is the midpoint of AE, prove that ar(∆BOE) = ar(∆ABC).

In the adjoining figure, ABCD is a parallelogram and O is any point on the diagonal AC.

Show that ar(∆AOB) = ar(∆AOD).

P.Q.R.S are respectively the midpoints of the sides AB, BC, CD and DA of ‖ gm ABCD. Show that PQRS is a parallelogram and also show that

Ar(‖gm PQRS) = x ar(‖gm ABCD).

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.

Show that ar(pentagon ABCDE) = ar(∆DGF).

Prove that a median divides a triangle into two triangles of equal area.

Show that a diagonal divides a parallelogram into two triangles of equal area.

The base BC of ∆ABC is divided at D such BD = DC. Prove that ar(∆ABD) = x ar(∆ABC).

In the adjoining figure, the points D divides the

Side BC of ∆ABC in the ratio m:n. prove that area(∆ABD): area(∆ABC) = m:n

Out of the following given figures which are on the same base but not between the same parallels?

In which of the following figures, you find polynomials on the same base and between the same parallels?

The median of a triangle divides it into two

The area of quadrilateral ABCD in the given figure is

The area of trapezium ABCD in the given figure is

In the given figure, ABCD is a ‖gm in which AB = CD = 5cm and BD⊥DC such that BD = 6.8cm. Then, the area of ‖gm ABCD = ?

In the given figure, ABCD is a ‖gm in which diagonals AC and BD intersect at O. If ar(‖gm ABCD) is 52cm², then the ar(∆OAB) = ?

In the given figure, ABCD is a ‖gm in which DL ⊥ AB. If AB = 10cm and DL = 4cm, then the ar(‖gm ABCD) = ?

In ‖gm ABCD, it is given that AB = 10cm, DL ⊥ AB and BM ⊥ AD such that DL = 6cm and BM = 8cm. Then, AD = ?

The lengths of the diagonals of a rhombus are 12cm and 16cm. The area of the rhombus is

Two parallel sides of a trapezium are 12cm and 8cm long and the distance between them

6.5cm. The area of the trapezium is

In the given figure ABCD is a trapezium such that AL ⊥ DC and BM ⊥ DC. If AB = 7cm, BC = AD = 5cm and AL = BM = 4cm, then ar(trap. ABCD) = ?

In a quadrilateral ABCD, it is given that BD = 16cm. If AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 7cm, then ar(quad.ABCD) = ?

ABCD is a rhombus in which ∠C = 60°. Then, AC : BD = ?

In the given figure ABCD and ABFE are parallelograms such that ar(quad. EABC) = 17cm² and ar(‖gm ABCD) = 25cm². Than, ar(∆BCF) = ?

∆ABC and ∆BDE are two equilateral triangles such that D is the midpoint of BC. Then,

ar(∆BDE): ar(∆ABC) = ?

In a ‖gm ABCD, if Point P and Q are midpoints of AB and CD respectively and ar(‖gm ABCD) = 16cm², then ar(‖gmAPQD) = ?

The figure formed by joining the midpoints of the adjacent sides of a rectangle of sides 8cm and 6cm is a

In ∆ABC, if D is the midpoint of BC and E is the midpoint of AD, then ar(∆BED) = ?

The vertex A of ∆ABC is joined to a point D on BC. If E is the midpoint of AD, then ar(∆BEC) = ?

In ∆ABC, it given that D is the midpoint of BC; E is the midpoint of BD and O is the midpoint of AE. Then ar(∆BOE) = ?

If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the parallelogram is

In the given figure ABCD is a trapezium in which AB‖DC such that AB = a cm and DC = b cm. If E and F are the midpoints of AD and BC respectively. Then, ar (ABFE) : ar(EFCD) = ?

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD is

In the given figure, a ‖gm ABCD and a rectangle ABEF are of equal area. Then,

In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. If AD = 25cm, then area of the rectangle is

Look at the statements given below:

(I) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.

(II) In a ‖gm ABCD, it is given that AB = 10cm. The altitudes DE on AB and BF on AD being 6cm and 8cm respectively, then AD = 7.5 cm.

(III) Area of a ‖gm = x base x altitude.

Which is true?

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

Which of the following is a false statement?

(A) A median of a triangle divides it into two triangles of equal areas.

(B) The diagonals of a ‖gm divide it into four triangles of equal areas.

(C) In a ∆ABC, if E is the midpoint of median AD, then ar(∆BED) = ar(∆ABC).

(D) In a trap. ABCD, it is given that AB‖DC and the diagonals AC and BD intersect at O. Then, ar(∆AOB) = ar(∆COD).

Which of the following is a false statement?

A) If the diagonals of a rhombus are 18cm and 14cm, then its area is 126cm².

B) Area of a ‖gm = x base x corresponding height.

C) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.

D) If the area of a ‖ gm with one side 24cm and corresponding height h cm is 192cm², then h = 8cm.

The area of ‖ gm ABCD is

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area. Then, ABCD

In the given figure, ABCD and ABPQ are two parallelograms and M is a point on AQ and BMP is a triangle.

Then, ar(∆BMP) = ar(‖gm ABCD).

The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to

Let ABCD be a ‖ gm in which DL ⊥ AB and BM ⊥ AD such that AD = 6 cm, BM = 10 and DL = 8 cm. Find AB.

Find the area of the trapezium whose parallel sides are 14 cm and 10 cm and whose height is 6 cm.

Show that the median of a triangle divides it into two triangles of equal area.

Prove that area of a triangle = X base X altitude.

In the adjoining figure, ABCD is a quadrilateral in which diagonal BD = 14cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove that ar(∆ABP) = ar(quad. ABCD).

In the given figure, ABCD is a quadrilateral and BE ‖ AC and also BE meets DC produced at E. Show that the area of ∆ADE is equal to the area of quad. ABCD.

In the given figure, area of ‖ gm ABCD is 80 cm².

Find (i) ar(‖gm ABEF)

(ii) ar(∆ABD) and (iii) ar(∆BEF).

In trapezium ABCD, AB‖DC and L is the midpoint of BC. Through L, a line PQ ‖ AD has been drawn which meets AB in Point P and DC produced in Q.

Prove that ar(trap. ABCD) = ar(‖gm APQD).

In the adjoining figure, ABCD is a ‖ gm and O is a point on the diagonal AC. Prove that ar(∆AOB) = ar(∆AOD).

∆ ABC and ∆BDE are two equilateral triangles such that D(E) is the midpoint of BC. Then, prove that ar(∆BDE) = ar(∆ABC).

In ∆ABC, D is the midpoint of AB and P Point is any point on BC. If CQ ‖ PD meets AB in Q, then prove that ar(∆BPQ) = ar(∆ABC).

Show that the diagonals of a ‖ gm divide into four triangles of equal area.

In the given figure, BD ‖ CA, E is the midpoint of CA and BD = CA.

Prove that ar(∆ABC) = 2×ar(∆DBC).

The given figure shows a pentagon ABCDE in which EG, drawn parallel to DA, meets BA produced at G and CF drawn parallel to DB meets AB produced at F.

Show that ar(pentagon ABCDE) = ar(∆DGF).

In the adjoining figure, the point D divides the side BC of ∆ABC in the ratio m:n. Prove that ar(∆ABD): ar(∆ADC) = m:n.

In the give figure, X and Y are the midpoints of AC and AB respectively, QP ‖ BC and CYQ and BXP are straight lines. Prove that ar(∆ABP) = ar(∆ACQ).