Area of Triangle (Base Length and Height Are Known)

Q. Question 10
Find the area of the trapezium PQRS with height PQ given in the figure given below:

Q.

The perimeter of a right triangle is $144cm$ and its hypotenuse measure $65cm$. Find the lengths of the other sides and calculate its area using heron's formula.

Q.

If the area of a triangle is 48cm² and its base is 8cm. Then find the height of the triangle.

1. 6 cm

2. 12 cm

3. 9 cm

4. 24 cm

Q.

Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.

Q.

The difference between two adjoining sides containing right angle of a right angled triangle is 14cm . The area of a tristria is 120cm . Verify the area using herons formula.

Q. The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. The length of the perpendicular from the opposite vertex to the side whose length is 13 cm is $\frac{m}{13}$. Find the value of $m÷10$.

1. 6
2. 60
3. 5
4. 13

Q.

If each side of a triangle is tripled then find its percentage increased in area?

Q.

ABC is a triangle in which D is the mid point of BC and E is the mid point of AD. Then area (∆BED) is equal to

1. 

2. 

3. 

4. 

Q. Question 1
An isosceles right triangle has area $8c{m}^2$. The length of its hypotenuse is

Q.

If the height of a triangle is $10cm$ and its area is $40{cm}^2$, then the base of the triangle is $6cm$.

1. 8cm

2. 18cm

Q.

If the base of a triangular field is 12cm and height is 14cm.What will be the area of the triangle in ${cm}^2$?

Q. If every side of a triangle is doubled, then increase in the area of the triangle is

(a) $100\sqrt{2}\%$

(b) 200%

(c) 300%

(d) 400%

Q. If the base and height of a triangle are 10 cm and 5 cm respectively, then find the area of the triangle.

1. 50 sq cm
2. 30 sq cm
3. 25 sq cm
4. 20 sq cm

Q.

What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units?

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

2. $\frac{lw}{3}$

3. $\frac{lw}{4}$

4. $\frac{lw}{6}$

Q.

Area of a triangle $=\frac{1}{2}\times base\times$______.

Q.

Find the area of the quadrilateral (in sq.units) as shown in the figure below. $\angle$EAB = $\angle$AED = 90°. Given that: AB + AE = 4 units and EC = 7 units.

1. 18
2. 9
3. 22
4. 16

Q. In the given figure, AB = 8 cm, BC = 6 cm, AC = 10 cm, then the area of $\Delta ABC$ is equal to

1. $(\sqrt{3}+20)c{m}^2$
2. $(20\sqrt{3}+5)c{m}^2$
3. $(24-\sqrt{3})c{m}^2$
4. $24c{m}^2$

Q. 86.Two sides of a triangle are 10 cm and 5 cm in length and the length of the median to the third side is 6.5 cm. If the area of the triangle is Find the value of p.

Q. Question 53

Fill in the blanks to make the statement true.

Area of triangle = $\frac{1}{2}\times base\times$ ___.

Q. There is a point inside an equilateral triangle which at dis†an ces 1, 2 and 3 from three sides. The area of the triangle is 1. not determinable 2. 6 3. 6\sqrt3 4. 12\sqrt3

Q. In the equilateral triangle ABC , the points D and E are on AC and AB respectively , such that BD and CE intersect at 0, and the area of the quadrilateral ADoE is equal to area of triangle BoC find angleBOE? f

Q.

Find the area of triangle whose base is $5\mathrm{cm}$ and height is $6\mathrm{cm}$. Find the area of triangle.

Q. The length of two sides of an isoscele traingle are $5cm$ and $8cm$, find perimeter of triangle.

1. $5\text{cm}$
2. $21\text{cm}$
3. $13\text{cm}$
4. $8\text{cm}$

Q. 13 Any point D is taken on the base BC of a triangle ABC and it is produced to e such that d e equal to ad. show that show that the area of triangle BCE is equal to the area of triangle ABC

Q.

The area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is (A) $r^2$ $sq.units$ (B) $\frac{1}{2}{r}^2$ $sq.units$ (C) $2r^2$ $sq.units$

(D) $\sqrt{2}{r}^2$$sq.units$

Q. The area of an isosceles triangle ABC is 48 cm${}^2$, where AB = AC. If the perimeter of the triangle and its altitude AD on BC are 32 cm and 8 cm respectively, then the length of the equal sides is equal to

1. 8 cm
2. 10 cm
3. 12 cm
4. 13 cm

Q. Refer to the isosceles triangle shown, where AB = AC = x. AE is the perpendicular such that AE = p and BC = d. Find the length of CD ___.
(Given that AB$\perp$CD and also, d = 2x)

Q.

If the area of an equilateral triangle is $25\sqrt{3}c{m}^2$, then its perimeter = ____ cm.

1. 10

2. 30

3. 45

4. 60

Q.

Find the area of a triangle whose base is $18cm$ and altitude is $10cm$.

Q. A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.