Area of a Triangle

Q.

How do you simplify the expression $\frac{1}{cotx}$?

Q.

How do you simplify the expression $\frac{1}{\tan x}$?

Q.

The Perimeter of a triangle $ABC$ is $6$ times the Arithmetic Mean of the sines of its angles. If the side $a$ is $1$, Then the Angle $A$ is_____.

Q.

Prove that $\frac{(cotA-\cos A)}{(cotA+\cos A)}=\frac{(\cos ecA-1)}{(\cos ecA+1)}$

Q. If AB = BC, AC=12 cm, and area of Δ BEC is 72 $c{m}^2$, find area of parallelogram ACEF.

1. 288 $c{m}^2$
2. 144 $c{m}^2$
3. 576 $c{m}^2$
4. 216 $c{m}^2$

Q.

The integral ${\int }_{\frac{\mathrm{\pi }}{6}}^{\frac{\mathrm{\pi }}{3}}{\tan }^{3}x·{\sin }^{2}3x\left(2{\sec }^{2}x·{\sin }^{2}3x+3\tan x·\sin 6x\right)dx$ is equal to

1. $\frac{9}{2}$

2. $-\frac{1}{18}$

3. $-\frac{1}{9}$

4. $\frac{7}{18}$

Q.

Two angles of a triangle are ${50}^{\circ }$ and ${70}^{\circ }$. The third angle is:

1. 70^o

2. 50^o

3. 120^o

4. 60^o

Q.

The angle of elevation of the top of the tower observed from each of the three points $AB$and $C$ on the ground forming a triangle is the same i.e.$\angle \alpha$. If $R$ is the circumradius of the$∆ABC$, then the height of the tower is

1. $R\sin \alpha$

2. $R\cos \alpha$

3. $Rcot\alpha$

4. $R\tan \alpha$

Q. In a triangle, the base is double the height and area is given to be 400 sq cm. Find its base and height.

1. 10 cm, 20 cm
2. 20 cm, 10 cm
3. 40 cm, 20 cm
4. 20 cm, 40 cm

Q.

Prove that $\cos 2x.\mathrm{co}s\left(\frac{x}{2}\right)-\cos 3x.\cos \left(\frac{9x}{2}\right)=\sin 5x.\sin \left(\frac{5x}{2}\right)$

Q.

If the area of a triangle is $49c{m}^2$ and its base is double the corresponding height, then find the height of the triangle.

1. 6 cm

2. 9 cm

3. 24 cm

4. 7 cm

Q. What is the area of a triangle with base 4.8 cm and height 3.6 cm ?

Q.

In triangle PQR, PR = 8 cm, QR = 8 cm and PL = 5 cm. Find the area of triangle PQR.

1. 10

2. 15

3. 20

4. 5

Q. what is the area of a triangle with base 6 cm and altitude 4.5 CM

Q.

Calculate the area of an equilateral triangle whose height is $20cm$. Find the area of triangle whose sides are $17cm$ , $8cm$ and $15cm$ .

Q.

Question 85

In the figures, perimeter of $\Delta ABC$ = perimeter of $\Delta PQR$. Find the area of $\Delta ABC.$

Q.

In the following figure, find the area of the shaded portion:

Q. A triangle has a base which is equal to twice its height. If the area is $36c{m}^2$, what is its height?

1. 18 cm
2. 36 cm
3. 6 cm
4. 12 cm

Q. ABCD is a rectangle with dimensions 24 m by 16 m. AFD is a triangle such that EF is perpendicular AD and EF = 10 m. Calculate the area of the shaded portion.

Q.

Question 128

4 squares each of the side 10 cm have been cut from each corner of a rectangular sheet of paper of size 100 cm $\times$ 80 cm. From the remaining piece of paper, an isosceles right triangle is removed whose equal sides are each of 10 cm length. Find the area of the remaining part of the paper.

Q. Find the area of an iscoceles triangle whose base is 16 cm, and length of each side = 10 cm.

Q.

If CD is a median of $\Delta$ABC, then

1. AD = DB

2. ∠ACD = ∠DCB

3. ∠CAD = ∠CBD

4. CD = AD

Q. Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Q. Question 41

Fill in the blanks to make the statement true.

In the given figure, area of parallelogram BCEF is___ $c{m}^2$, where ACDF is a rectangle.

Q. If a parallelogram having area $48{\text{cm}}^2$ and height 6 cm is transformed into a triangle with the same base and area as that of the parallelogram, then what is the height of the triangle?

1. 9 cm
2. 12 cm
3. 18 cm
4. 24 cm

Q.

Find the side length of an equilateral triangle whose perimeter is 9 cm.

1. 9 cm

2. 6 cm

3. 3 cm

4. 81 cm

Q.

Find the area of figure given below (all dimensions in inches).

Q.

Question 15

Area of $\Delta PQR$ is $100c{m}^2$ as shown in the figure below. If altitude QT is 10 cm, then its base PR is

(a) 20 cm
(b) 15 cm
(c) 10 cm
(d) 5 cm

Q.

Question 2 (a)
Draw rough sketches for the following:
In $\Delta$ABC, BE is a median.

Q.

In the following figure, the relation between the angles 1, 2 and 3 is:

1. 

2. 

3. 

4.