Triangles on the Same Base and Between the Same Parallels

Q. The altitude of an triangle will lie outside the triangle.

1. acute-angled
2. obtuse-angled
3. right-angled

Q. A triangle has altitude(s).

1. 1
2. 2
3. 3
4. infinite

Q. ABCD ia a parallelogram. P is any point on CD. If $ar\left(\Delta DPA\right)=15c{m}^{2}andar\left(\Delta APC\right)=20c{m}^2$, then find the ar $\left(\Delta APB\right).$

1. 
2. 
3. 
4. 

Q. Find the area of shaded region, if the side of each square is 2m.

1. 20$m^2$
2. 40$m^2$
3. 60$m^2$
4. 80$m^2$

Q.
In the figure, what is ratio of area of $△FAR\text{and area of parallelogram CART}?.$

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

Q.

PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. If BE || AC and CF || AB meet PQ at E and F respectively. If the base and altitude of ΔABC are 6 cm and 8 cm respectively, the area of ΔACF is ___

1. 24

2. 48

3. 96

4. 12

Q. Which of the following shows the possible dimensions of a triangle of area $100m^2?$

1. Base (b) = 20 m, Height (h) =10 m
2. Base (b) = 25 m, Height (h) =10 m
3. Base (b) = 25 m, Height (h) =8 m
4. Base (b) = 50 m, Height (h) =10 m

Q.

If the given figure shows parallelogram ABCD. Points P and Q trisect the side AB, then ____.

1. $Area\left(△DPQ\right)=\frac{1}{3}\times Area\left(ABCD\right)$

2. $Area\left(△DPQ\right)=\frac{2}{5}\times Area\left(ABCD\right)$

3. $Area\left(△DPQ\right)=\frac{1}{6}\times Area\left(ABCD\right)$

4. $Area\left(△DPQ\right)=\frac{4}{5}\times Area\left(ABCD\right)$

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.
In the figure parallelogram FAST and rectangle BASE are on the same base AS and have equal areas.
Which of the following statement is true for parallelogram FAST and rectangle BASE?

1. They have equal perimeter.
2. Perimeter of rectangle is greater than that of parallelogram.
3. Perimeter of parallelogram is greater than that of rectangle.
4. Perimeter of parallelogram is smaller than that of rectangle.

Q.

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

1. $16c{m}^2$

2. $26c{m}^2$

3. $36c{m}^2$

4. $46c{m}^2$

Q. In the given figure, If the area of parallelogram BIPS is $144m^2,$
then the area of $\Delta NPSis$ _____.

1. $144m^2$
2. $288m^2$
3. $72m^2$
4. $36m^2$

Q.

What is the ratio $\frac{AC}{BC}$ for the following construction method:
A line segment AB is drawn.
A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at $A_1$, $A_2$… $A_{12}$.
A line is drawn from $A_{12}$ to B and a line parallel to $A_{12}$B is drawn, passing through the point $A_6$ and cutting AB at C

1. 1:2

2. 1:1

3. 2:1

4. 3:1

Q.

Fill in the blanks to make the statements true.

(a) In right triangle the hypotenuse is the __________ side.

(b) The sum of three altitudes of a triangle is __________ than its perimeter.

(c) The sum of any two sides of a triangle is __________ than the third side.

(d) If two angles of a triangle are unequal, then the smaller angle has the __________ side opposite to it.

(e) Difference of any two sides of triangle is __________ than the third side.

(f) If two sides of a triangle are unequal, then the larger side has ___________angle opposite to it.

Q.

Find the area of the above shown figure( in m²). Where ABE is an equilateral triangle, ABCD is a rectangle, arc BC, and arc AD are semi circle.

1. 351.7

2. 400

3. 252.45

4. 451.7

Q. Which of the following triangles have half the area of parallelogram KTRL.

1. $\Delta KTM$
2. $\Delta MTR$
3. $\Delta NTR$
4. $\Delta RMN$

Q.

In the given figure, AP $\parallel$ BQ $\parallel$ CR. What will be ($△$AQC)?

1. ar ($△$PBR)

2. ar ($△$PQA).

3. ar ($△$ABQ).

4. ar ($△$CQR).

Q.

If $\overleftrightarrow{AD}||\overleftrightarrow{BC},$ then area $\left(\Delta ABC\right)$ = area $\left(\Delta BEC\right)$. = area $\left(\Delta DBC\right)$.

1. True

2. False

Q. Which of the following triangles is half the area of parallelogram PAIN.

1. $\Delta AIN$
2. $\Delta DIP$
3. $\Delta PIN$
4. $\Delta AIP$

Q. Ali and Cassim need to cross the forest, which is rectangular in shape, to reach the treasure cave. The forest's side lengths are $(5.6\times {10}^8)\text{and}(3.3\times {10}^6)$. What is the area of the forest?

1. $1.848\times {10}^{15}$
2. $18.48\times {10}^{15}$
3. $1.848\times {10}^9$
4. $1.848\times {10}^{15}$