Area of a Triangle

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 $c{m}^2$ is __________.

1. Rs.2.16

2. Rs.2.48

3. Rs.3.00

4. Rs.200

Q. The area of an equilateral triangle is $49\sqrt{3}c{m}^2$. 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.

1. $10.77c{m}^2.$
2. $7.77c{m}^2.$
3. $9.77c{m}^2.$
4. $8.77c{m}^2.$

Q. Some measures are given in the adjacent figure, find the area of ☐ABCD.

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 $144\sqrt{3}c{m}^2$; find its perimeter.

Area of an equilateral triangle

$=\frac{\sqrt{3}}{4}\times (side{)}^2$ and its perimeter $=3\times$ side

Q.

The figure shows an equilateral $\Delta ABC$ of side 10 cm and a right angle $\Delta BDC$ whose side BD = 8 cm and $\angle D={90}^{\circ }$.

The area of the shaded portion is ___ $c{m}^2$.

1. 18.3

2. 19.3

3. 20

4. 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 ☐ 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:

1. $24c{m}^2$

2. $26c{m}^2$

3. $30c{m}^2$

4. $35c{m}^2$

Q. The base of an isosceles triangle is $\frac{4}{3}$ cm. The perimeter of the triangle is $4\frac{2}{15}$ cm. What is the length of either of the remaining equal sides?

1. Length of either of the remaining equal sides is $2\frac{3}{4}$ cm
2. Length of either of the remaining equal sides is $5\frac{1}{6}$ cm
3. Length of either of the remaining equal sides is $1\frac{1}{3}$ cm
4. Length of either of the remaining equal sides is $1\frac{2}{5}$ 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 $\Delta ABC.$

(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 $67.5m^2$; 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 $=\frac{Costofthefield}{Rate}=\frac{49,57,200}{36,720}$ hectare

=135 hectare

$=135\times 10,000$ sq. m=1350000 $m^2.$

Q.

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

1. True

2. False

Q. Find the area of the quadrilateral shown below.

1. 46 $c{m}^2$
2. 40 $c{m}^2$
3. 36 $c{m}^2$
4. 42 $c{m}^2$

Q. It is given that $\Delta ABC\sim \Delta EDF$ 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 $49c{m}^2$ and its base is double the height, then find the height of the triangle.

1. 6 cm

2. 9 cm

3. 24 cm

4. 7 cm

Q. In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm${}^2$) of the quadrilateral ABCD.

1. 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 $20c{m}^2$ 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 $153.76c{m}^2$. Find the area of the shaded part if P, Q, R, S are the midpoints of the sides.

Q. Question 11
If $\Delta ABC\sim \Delta QRP,\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=\frac{9}{4}$, AB = 18 cm and BC = 15cm, then PR is equal to

(A) 10 cm
(B) 12 cm
(C) $\frac{20}{3}cm$
(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 $m^2$; find its base and height.

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

$\therefore \frac{1}{2}\times 4x\times 5x=40.$

Q.

What is the area(in ${cm}^2$) of this triangle?
___