Triangles between Same Parallels

Q. What is pi? Why do we use in circle? Why do we not use any other formula to find area or perimeter of circle?

Q.

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

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

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

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

4. area of triangle = area of parallelogram

Q.

The area of a parallelogram is 338 m square if its altitude is twice the corresponding base determine the base and altitude

Q.

ABCD is a parallelogram. E and F are the mid-Points of BC and AD respectively. Show that the segments BF and DE trisect the diagonal AC. [4 MARKS]

Q.

The area of isosceles right angled triangle is $16c{m}^2$ then the length of the hypotenuse is

1. $8cm$

2. $9cm$

3. $10cm$

4. $11cm$

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.

If the area of parallelogram ABCD is 54 square units, what is the area of parallelogram ABEF? [Given: O and P are the midpoints of AD and BC respectively]

1. 27 square units

2. 30 square units

3. 33 square units

4. 36 square units

Q.

AE || BC and D is the midpoint of BC. If area $△ABC$ = 84 square cm, what is the area of $△BDE$?

1. 21 square cm

2. 42 square cm

3. 63 square cm

4. 84 square cm

Q.

In a parallelogram ABCD, AB = 2 BC. If the length of the altitude corresponding to AB is 10 cm, what is the length of the altitude corresponding to BC?

1. 15 cm

2. 40 cm

3. 10 cm

4. 20 cm

Q.

ABCD is a parallelogram. P is any point on CD. If ar$\left(△DPA\right)=25c{m}^2$ and ar$\left(△APC\right)=40c{m}^2$, then area$\left(△APB\right)$is

1. $45c{m}^2$

2. $75c{m}^2$

3. $65c{m}^2$

4. $32c{m}^2$

Q.

ABCD is a parallelogram and P, Q are the midpoints of DC and AB respectively. Then, area of parallelogram AQPD is equal to area of triangle ADB.

1. True

2. False

Q.

In this figure AB $\parallel$ DC. Write two pairs of triangles having the same area.

1. $△ADB$ and $△ACB$
2. $△DCA$ and $△ADB$
3. $△DCA$ and $△DCB$
4. $△ADB$ and $△DCB$

Q.

$D,E\mathrm{and}F$are respectively the mid-points of sides $AB,BC\mathrm{and}CA$ of $\Delta ABC$. Find the ratio of the area of $\Delta DEF$ and $\Delta ABC$

Q. A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.

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

Q.

ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area of ($△$APB) is equal to

1. 15 cm²

2. 35 cm²

3. 50 cm²

4. 70 cm²

Q. $D,E$ and $F$ are respectively the mid-points of the sides $BC,CA$ and $AB$ of a $△ABC$. Show that
(i) $BDEF$ is a parallelogram
(ii) $ar\left(DEF\right)=\frac{1}{4}ar\left(ABC\right)$
(iii) $ar\left(BDEF\right)=\frac{1}{2}ar\left(ABC\right)$

Q.

In the given figure, ABQP and ABCD are two parallelograms on the same base AB. $\frac{AreaofparallelogramABCD}{AreaoftrianglePAB}isequalto:$

__

Q. ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area($△$APB) is

1. 15 $c{m}^2$
2. 35 $c{m}^2$
3. 70 $c{m}^2$
4. 50 $c{m}^2$

Q.

Which among the following is correct?
Parallelograms on the same base and between the same set of parallel lines:

1. have unequal areas

2. have the same perimeter

3. may have equal or unequal areas

4. have equal areas

Q.

If two triangles have equal area and stand on the same base, then the altitudes of the triangle are equal.

1. True

2. False

Q.

The median of any triangle bisects it into two triangles of equal areas.

1. True

2. False

Q.

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

1. Area of ∆BEC and ∆ BDC are equal.

2. (1/2)Area of BDEC = Area of ∆BDC

3. DE is parallel to BC

4. All of the above

Q. P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP,
Show that $ar\left(\Delta PBQ\right)=ar\left(\Delta ARC\right)$.

Q. Two triangles have the same base and between the same parallels. Area of one triangle is 36 $c{m}^2$. Area of 2nd triangle is ______.

1. 18 $c{m}^2$
2. 54 $c{m}^2$
3. 48 $c{m}^2$
4. 36 $c{m}^2$

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

Q. Sides of two similar triangles are in the ratio $4:9$. Areas of these triangles are in the ratio :

1. $4:9$
2. $81:16$
3. $2:3$
4. $16:81$

Q. In a triangle $ABC,E$ is the midpoint of median AD, show that $area△ABE=\frac{1}{4}area\left(△ABC\right)$

Q.

If AD is median of ΔABC and P is a point on AC such that ar(ΔADP) : ar(ΔABD) = 2 : 3, then ar(ΔPDC) : ar(ΔABC) is ______ .

1. 3 : 5
2. 1 : 6
3. 2 : 5
4. 1 : 5

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. In fig 9.27. ABCDE is a pentagon . A line through B parallel to C meets DC produced at F . Show that
(i) ar(ACB) = ar(ACF)
(ii) ar(AEDF) = ar(ABCDE)