# Area of a Triangle

## Trending Questions

**Q.**

The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm2 is __________.

Rs.2.16

Rs.2.48

Rs.3.00

Rs.200

**Q.**The area of an equilateral triangle is 49√3 cm2. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circle.

- 10.77cm2.
- 7.77cm2.
- 9.77cm2.
- 8.77cm2.

**Q.**Some measures are given in the adjacent figure, find the area of āABCD.

**Q.**

A triangular park has sides $120m,80mand50m$. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of $Rs30perm$ leaving a space of $3m$ wide for a gate on one side.

**Q.**

Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.

**Q.**

The area of an equilateral tringle is 144√3cm2; find its perimeter.

Area of an equilateral triangle

=√34×(side)2 and its perimeter =3× side

**Q.**

The figure shows an equilateral ΔABC of side 10 cm and a right angle ΔBDC whose side BD = 8 cm and ∠D=90∘.

The area of the shaded portion is

18.3

19.3

20

16

**Q.**

Question 67

State whether the statement is True or False.

Triangles having the same base have equal area.

**Q.**Look at the measures shown in the adjacent figure and find the area of ā PQRS.

**Q.**

Two sides of a triangle are 6 cm and 8 cm. If height of the triangle corresponding to 6 cm side is 4 cm; find:

(i) are of the triangle

(ii) height of the triangle corresponding to 8 cm side.

**Q.**

The sides of a triangle are 5cm, 12cm and 13cm, then its area is:

24 cm2

26 cm2

30 cm2

35 cm2

**Q.**The base of an isosceles triangle is 43 cm. The perimeter of the triangle is 4215 cm. What is the length of either of the remaining equal sides?

- Length of either of the remaining equal sides is 234 cm
- Length of either of the remaining equal sides is 516 cm
- Length of either of the remaining equal sides is 113 cm
- Length of either of the remaining equal sides is 125 cm

**Q.**

Two sides of a triangle are 6-4 m and 4-8 m. If height of the triangle corresponding to 4-8 m side id 6 m; find:

(i) Area of the triangle;

(ii) Height of the triangle corresponding to 6-4 m side

**Q.**

Find the area of the right-angled triangle with hypotenuse 40 cm and one of the other two sides 25 cm.

**Q.**

Use the information given in the adjoining figure to find:

(i)The length of AC.

(ii)The are a of ΔABC.

(iii)The length of BD, correct to one decimal place.

**Q.**

The base and the height of a triangle are in the ratio 5 : 3. If the area of the triangle is 67.5m2; find its base and height

**Q.**

The altitude and the base of a triangular field are in the ratio 6 : 5. If its cost is Rs 49, 57, 200 at the rate of Rs 36, 720 per hectare and 1 hectare =10, 000 sq. m, find (in metre) dimensions of the field.

Area of the given triangular field =CostofthefieldRate=49, 57, 20036, 720 hectare

=135 hectare

=135×10, 000 sq. m=1350000 m2.

**Q.**

Area of a quadrilateral can be found by splitting it into triangles.

True

False

**Q.**Find the area of the quadrilateral shown below.

- 46 cm2
- 40 cm2
- 36 cm2
- 42 cm2

**Q.**It is given that ΔABC∼ΔEDF such that AB = 5cm, AC = 7cm, DF = 15cm and DE = 12cm. find the lengths of the remaining sides of the triangles.

**Q.**

If the area of a triangle is 49 cm2 and its base is double the height, then find the height of the triangle.

6 cm

9 cm

24 cm

7 cm

**Q.**In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm2) of the quadrilateral ABCD.

- 40

**Q.**

Consider the figure below:

If AB = 5 cm; QR = 7cm; then find the value of AC (in cm.), if the perimeter of △ABC is 18cm.

**Q.**

If the sum of base and height of a right triangle is $20cm$, what is the maximum area of the triangle?

**Q.**Find area of quadrilateral ABCD

**Q.**

**Question 20**

Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is

(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

**Q.**ABCD is a square of area 153.76 cm2. Find the area of the shaded part if P, Q, R, S are the midpoints of the sides.

**Q.**Question 11

If ΔABC∼ΔQRP, ar(ΔABC)ar(ΔPQR)=94, AB = 18 cm and BC = 15cm, then PR is equal to

(A) 10 cm

(B) 12 cm

(C) 203 cm

(D) 8cm

**Q.**

The base and the height of a triangle are in the ratio 4 : 5. If the area of the triangle is 40 m2; find its base and height.

Let base be 4x m and height be 5x m.

∴12×4x×5x=40.

**Q.**

What is the area(in cm2) of this triangle?