Area of Triangle and Rectangle on the Same Base and between the Same Parallels

Q.

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

1. True

2. False

Q.

Diagonals of a square divide it into 4 congruent triangles. Are all these triangles congruent to each other? If yes, using which criterion?

Q. The height of the two buildings is 34 m and 29 m respectively. The distance between their top is 13 m, then the distance between the two buildings is.

1. $16m$
2. $13m$
3. $12m$
4. $14m$

Q.

The base and height of the triangle are in the ratio 3:2. If the area of the triangle is 243 cm${}^2$, find the base and height of the triangle.

1. Base = 18 cm, Height = 27 cm

2. Base = 12 cm, Height = 18 cm

3. Base = 27 cm, Height = 54 cm

4. Base = 27 cm, Height = 18 cm

Q.

Why does cross product give area of a parallelogram ?

Q. In the figure given below, the area of the triangle ABC is $16c{m}^2$. What will be the area of the triangle ABD?

1. $6c{m}^2$
2. $8c{m}^2$
3. $16c{m}^2$
4. $32c{m}^2$

Q.

If 8, x, 17 form a Pythagorean triplet with 17 being the largest number. The value of x is _____.

1. 8

2. 9

3. 10

4. 15

Q.

In the figure $\angle PSQ={90}^{\circ },$
PQ = 10 cm, QS = 6 cm & RQ = 9 cm.
Calculate the length of PR (in cm).

1. 17

Q. Area of the triangle considering BC as a base is ________.

1. $15c{m}^2$
2. $36c{m}^2$
3. $11c{m}^2$
4. $9c{m}^2$

Q.

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

1. True

2. False

Q.

Given below are measurements of some parts of pair of triangles which of the pair of two triangles are congruent to each other.

1. ∠B = 90^o, AB = 4, AC = 5; ∠P = 90^o, PQ = 4, PR = 5

2. ∠B = 90^o, AB = 3, AC = 5; ∠P = 90^o, PQ = 3, PR = 5

3. ∠A = 90^o, AB = 3, AC = 5; ∠P = 90^o, PQ = 3, PR = 5

4. ∠C = 90^o, AB = 3, AC = 5; ∠P = 90^o, PQ = 4, PR = 5

Q.

Two triangles are congruent if they have ___.

1. Same name

2. Equal measures

3. Unequal measures

4. Same direction

Q.

In the image, if you mark the points like this:

What is the length of BF?

1. 40 m

2. 80 m

3. 20 m

4. 10 m

Q. Match the triangles of equal area from the given figures.

1. Triangles ADF & BDF
2. Triangles ADG & BDG
3. Triangles ADE & CDE

Q. The above triangle is right angled triangle with hypotenuse equal to $10cm.$ Find the length of the sides containing the right angle.

1. $6cm,8cm$
2. $4cm,6cm$
3. $6cm,10cm$
4. $8cm,10cm$

Q.

What is the ratio of the area of parallelogram ABCD to the sum of areas of $\Delta ABE$ and $\Delta ABF?$

1. 2:1

2. 1:3

3. 1:2

4. 1:1

Q.

Parallelograms ABCD and FBCE lie on the same base (or equal bases). If area of parallelogram ABCD = 14 square units, find the area of parallelogram FBCE.

1. 40m

2. 50m

3. 60m

4. 70m

Q. Find the area in square metres of the parallelogram whose base and altitudes are as under:
(i) Base = 15 dm, altitude = 6.4 dm
(ii) Base = 1 m 40 cm, altitude = 60 cm

Q. The hypotenuse is the longest side of a right angled triangle.

1. False
2. True

Q. In the following triplet pythagorean ? show working
(18, 79, 82)

Q. 𝐴𝐵𝐶 is a triangle, right-angled at 𝐶. If 𝐴𝐵 = 25 𝑐𝑚 and 𝐴𝐶 = 7 𝑐𝑚, find 𝐵𝐶.

Q.

The following are the lengths of sides of various triangles. Which of them are right triangles?

$30cm,40cm,50cm$

Q. The area of a triangle of baselength $4cm$ and height $3.5cm$ is $7c{m}^2$

1. True
2. False

Q. Two sides of a parallelogram are 20 cm and 25 cm. If the altitude corresponding to the sides of length 25 cm is 10 cm, find the altitude corresponding to the other pair of sides.

Q.

Let $a,b,c$ be the lengths of the sides of a right angled triangle, the hypotenuse having the length $c$, then $a+b$ is

1. $>2c$

2. $<\sqrt{2}c$

3. $>\sqrt{2}c$

4. $<2c$

Q.

Area of a triangle with the same base and height as a parallelogram is ___ the area of the parallelogram.

1. half

2. twice

3. equal to

4. thrice

Q. Find the area of the following triangle:

1. $3c{m}^2$
2. $8c{m}^2$
3. $5c{m}^2$
4. $9c{m}^2$

Q. Find the length of the hypotenuse of a right triangle, the other two sides of which measure $9cm$ and $12cm$.

Q. Find the sum:
$\frac{5}{4}+\left(\frac{-11}{4}\right)$

Q.

In the figure below, if DE = 2DC and the area of parallelogram ABDE = 20 square units. Find the area of ΔDBC (in square units).

1. 10
2. 4
3. 5
4. 6