Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

Q.

Radha made a picture of an airplane with colored paper as shown in Fig. Find the total area of the paper used.

Q.

In the rectangle ABCD, O is any point inside the rectangle. If area($△$AOD) = 30 $c{m}^2$ and area($△$BOC) = 60 $c{m}^2$, Find the area of the rectangle ABCD. [2 MARKS]

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

1. half
2. twice
3. one - third

Q.

ABC is a triangle in which D, E, F are the mid-points of BC, AC and AB respectively. If Area (ΔABC) = 32 cm², then area of trapezium BFEC is ______

1. 8 $c{m}^2$
2. 16 $c{m}^2$
3. 24 $c{m}^2$
4. 32 $c{m}^2$

Q. Find area of the triangle if the sides of the triangle are in the ratio 12:17:25 and the perimeter is 270 m.

1. 2250

Q.

In the given figure, $ABCD$ is a parallelogram, then $ar(△AFB)$ is

Q.

P is the vertex of cuboid and Q, R and S are three points on the adjacent edges passing through P as shown. PQ = PR = 2 cm and PS = 1 cm. Then the area of $\Delta QRS\left(inc{m}^2\right)$ is:

1. $\frac{\sqrt{15}}{4}$

2. $\frac{5}{2}$

3. $\sqrt{6}$

4. $2\sqrt{2}$

Q.

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 $c{m}^2$ and ar(ABFE) = 18 $c{m}^2$, then ar (EFCD) [in $c{m}^2$] is

__

Q.

Question 3
The area of the parallelogram ABCD is $90c{m}^2$.
Find
a) ar (ABEF)
b) ar ($\Delta$ABD)
c) ar ($\Delta$BEF)

Q.

Diagonals AC and BD of trapezium ABCD in which AB || DC, intersect each other at O. The triangle which is equal in area to triangle BOC is

1. ΔAOB
2. ΔDOC
3. ΔAOD
4. ΔADC

Q.

The sides of a triangle are in the ratio $5:12:13$ and its perimeter is $150cm$. The area of the triangle is

1. $750c{m}^2$

2. $375c{m}^2$

3. $250c{m}^2$

4. $500c{m}^2$

Q.

PQRS is a parallelogram with PS = 4 cm and AR $\parallel$ PB. If Area of triangle APS = 48 $c{m}^2$, find the height of triangle QRB. [2 MARKS]

Q.

In the figure shown, area of ΔAXS is equal to half the area of the parallelogram PQRS

1. True

2. False

Q. A triangle ABC and a parallelogram ABDF lie on the same base AB and between the same parallels AB and DF. If the area of the triangle is $24c{m}^2$, what will be the area of the parallelogram ?

Q.

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

1. False

2. True

Q.

If a triangle and a parallelogram are on the same base and between the same parallels, then _____.

1. area of triangle = $\frac{1}{4}\times areaofparallelogram$

2. area of triangle = $\frac{1}{3}\times areaofparallelogram$

3. area of triangle = area of parallelogram

4. area of triangle = $\frac{1}{2}\times areaofparallelogram$

Q.

If the area of parallelogram PQRS is 32 cm² and line XY || AS , then the area of triangle ACS is____

1. 32 $c{m}^2$

2. Data Insufficient

3. 8 $c{m}^2$

4. 16 $c{m}^2$

Q. Two triangles ALM and BLM have same base LM = 6cm. These two triangles have an equal area of $24c{m}^2$. The distance between their altitudes is PQ. If PQ is equal to the length of one of the altitudes then the area of the quadrilateral formed by the altitudes and the base PQ is equal to:

1. $34c{m}^2$
2. $44c{m}^2$
3. $54c{m}^2$
4. $64c{m}^2$

Q. In fig, $ABCD$ is a parallelogram and $BC$ is produced to a point $Q$ such that $AD=CQ$. If $AQ$ intersect $DC$ at $P$, show that $ar\left(BPC\right)=ar\left(DPQ\right)$.

Q. All congruent triangles are equal in area.

1. True
2. False

Q.

In $\Delta$ ABC, DE is parallel to BC. Which of the following are correct?

1. $\frac{1}{2}\text{× Area of BDEC = Area of ΔBDC}$
2. Area of ∆BEC and ∆ BDC are equal.
3. Area of ∆DOB= Area of ∆EOC
4. Area of ∆DOB= Area of ∆EOD

Q.

(i)Write a property of diagonals of parallelogram.

(ii)ABCD is a parallelogram in which CD is produced to P.DC =6 cm and height BQ = 4 cm. Find the area of $\Delta APB$

Q.

Diagonals AC and BD of trapezium ABCD in which AB || DC, intersect each other at O. The triangle which is equal in area to triangle BOC is

1. ΔAOD
2. ΔDOC
3. ΔADC
4. ΔAOB

Q.

A point $ E$ is taken on the side $ BC$ of a parallelogram $ ABCD. AE$ and $ DC$ are produced to meet at $ F.$ Prove that ar $ (△ADF)=$ ar $ \left(ABFC\right)$

Q.

(i)Write a property of diagonals of parallelogram.

(ii)ABCD is a parallelogram in which CD is produced to P.DC =6 cm and height BQ = 4 cm. Find the area of \(\Delta APB\)

4cm 

Q.

​ABCD is a parallelogram and E and F are mid-points of AD and BC respectively. P is any point on AB. If area of ΔEDF=16 $c{m}^2$, then find the area of ( ΔAEP+ ΔBFP) [3 MARKS]

Q. $E,F,G$ and $H$ are the midpoints of the sides of a parallelogram $ABCD.$ SHow that area of quadrilateral $EFGH$ is half of the area of parallelogram $ABCD.$

Q.

In the given figure, ABCDE is a pentagon with AC = 5 cm. A line through B parallel to AC meets DC produced at F. If the altitude of triangle ABC (perpendicular to AC) is 6 cm. Find the area of triangle ACF.

1. 5 $c{m}^2$
2. 10 $c{m}^2$
3. 15 $c{m}^2$
4. 30 $c{m}^2$

Q.

The perimeter of a triangular field is $540m$ and its sides are in the ratio $25:17:12$ Find the area of the triangle. Also find the cost of ploughing the field at $Rs20$ per $10m^2$

Q.

AE || BC and D is the mid-point of BC. If area $△ABC$ = 84 $c{m}^2$, what is area of $△BDE$?

1. 42$c{m}^2$
2. 84 $c{m}^2$
3. 63 $c{m}^2$
4. 21$c{m}^2$