Area of Triangle

Q. If D and E are the mid-points of AB and AC of ΔABC respectively, then which of the following are not true?

1. DE $\parallel$ BC
2. 2 × DE = BC
3. DE = 2 × BC
4. DE = $\frac{1}{2}$ × BC

Q.

Of the given perimeter, the triangle having maximum area is

1. Isosceles triangle

2. Right angle triangle

3. Equilateral

4. None of these

Q.

If AD is the median of triangle ABC as shown in the figure, area of triangle ADC is________

1. 12 $c{m}^2$
2. 4 $c{m}^2$
3. 6 $c{m}^2$
4. 3 $c{m}^2$

Q.

If the area of a triangle is 48 $c{m}^2$ and its base is 8cm.Then find the height of the triangle.

1. 6cm

2. 24cm

3. 9cm

4. 12cm

Q.

The area of $△ABC$ is $8{cm}^2$ in which $AB=AC=4cm$ and $\angle A=90°$. Write True or False and justify your answer.

1. True
2. False

Q. Question 1
Write True or False and justify your answer:

The area of a triangle with base 4cm and height 6cm is 24 $c{m}^2$.

Q.

In a right angled triangle if the base is 3 cm and perpendicular is 4 cm.What is the area of that triangle?

1. 6cm²

2. 7cm²

3. 8cm²

4. 10cm²

Q. Show that the area of a triangle is half the product of its base (or any side) and the corresponding attitude (height).

Q. Find the area of the trapezium ABCD as given in the figure in which ADCE is a rectangle.

1. $35c{m}^2$
2. $55c{m}^2$
3. $45c{m}^2$
4. $40c{m}^2$

Q. Question 2
The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per $m^2$ per year. A company hired one of its walls for 3 months. How much rent did it pay?

Q.

The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?

1. Equilateral triangle of side 5 $\sqrt{3}$cm

2. Isosceles triangle, in which the equal sides measure 5 $\sqrt{2}$cm

3. Isosceles triangle, in which the unequal side measures 5 $\sqrt{2}$cm

4. Equilateral triangle of side 5cm

Q.

A trapezium with its parallel sides is in the ratio 16: 5 is cut from a rectangular whose sides measure 63 m and 5 m respectively. The area of the trapezium is $\frac{4}{15}$ of the rectangle. Find the difference between the lengths of the parallel sides of the trapezium.

1. 13.6 m

2. 18.4 m

3. 17.6 m​

4. None of these

Q. In trapezium ABED, C is the mid point of BE, ABCD is a rectangle with AB = 40 cm, BC = 20 cm. Find the area of trapezium ABED.

1. 1200 ${\text{cm}}^2$
2. 800 ${\text{cm}}^2$
3. 1600 ${\text{cm}}^2$
4. 400 ${\text{cm}}^2$

Q. In the figure, PQRS is a Parallelogram, QS is the diagonal, A is the mid-point of SR and D is the mid-point of RQ. If the area of $△$ ASQ $=20$ cm${}^2$, then find the area of $△ARD$.

Q.

Prove that two triangles on the same base (or equal bases) and between the same parallels are equal in area.
[4 MARKS]

Q.

What is the area of an equilateral triangle whose side is 8cm?Also find the corresponding altitude of the base. [4 MARKS]

Q.

If the base of a triangle is 24cm and height is 48cm.What will be the area of the triangle in $c{m}^2$?

1. 566

2. 576

3. 766

4. 676

Q.

What is the area of a right angled triangle if its sides are 6 cm, 8 cm and 10 cm?

1. 26 $c{m}^2$

2. 24 $c{m}^2$

3. 36 $c{m}^2$

4. 40 $c{m}^2$

Q. Question 2
Write True or False and justify your answer:

The area of a $\Delta ABC$ is 8 $c{m}^2$ in which AB = AC = 4 cm and $\angle A={90}^{\circ }$

Q. Without actual division. prove that $2x^4-5x^3+2x^2-x+2$ is divisible by $x^2-3x+2$

Q. Question 4
A Triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26cm, 28cm and 30cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Q.

The sides of a triangle are $35cm,$ $54cm$ and $61cm,$ respectively. The length of its longest altitude is

1. $16\sqrt{5}cm$
2. $10\sqrt{5}cm$
3. $24\sqrt{5}cm$
4. $28cm$

Q. Question 3
P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(APB) = ar(BQC).

Q. The mid-points of the sides BC, CA and AB of a ΔABC are D, E and F respectively. Which of the following is true?

1. Area of (DEF) = $\frac{1}{4}$ Area of $\Delta$ ABC
2. Area of (BDEF) = $\frac{1}{2}$ Area of $\Delta$ ABC
3. BDEF is a parallelogram
4. Area of (BDEF) = $\frac{1}{4}$ Area of $\Delta$ ABC

Q. The area of the obtuse angle triangle shown below is:

1. 17.5 sq. units
2. 25 sq. units
3. 14 sq. units
4. 15 sq. units

Q.

ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. If ar($△$ABC) = 16 $c{m}^2$, then
ar($△$DEF) is

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

Q.

$AD$ is the median of the $△ABC$. If the area of $△ABD=10$ sq. units, find the area of $△ABC$

1. $30$ sq. units
2. $40$ sq. units
3. $60$ sq. units
4. $20$ sq. units

Q. In the given $\Delta ABC$, Z is the mid-point of the median AD. If the area of $\Delta ABC$ is $18m^2$, find the area of $\Delta BZC$.

1. $7m^2$
2. $9m^2$
3. $6m^2$
4. $5m^2$

Q.

If the height and base of the right triangle is 12 cm and 9 cm resp., the area of the triangle is __ $c{m}^2$.

Q. The triangle formed by joining the mid-points of an equilateral triangle is triangle.

1. an equilateral
2. an isosceles
3. a scalene