Problems on Finding Area of Triangle and Parallelogram are available here for free. So, the students who wish to solve different types of problems in the area can refer to our page and solve the questions in a simple method. Use the formulas of triangle and parallelogram to find the area of the given questions. Read the entire article and learn how to solve the problems on finding area of triangle and parallelogram.

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## Finding Area of Triangle and Parallelogram Problems with Solutions

We have provided various types of questions on finding the area of triangles and parallelograms. This will help the students a lot to score good marks and also to improve their knowledge of the subject.

**Example 1.**

Find the Area of a triangle whose base is 6 cm and height is 8 cm.

**Solution:**

Given,

base = 6 cm

height = 8 cm

We know that,

Area of triangle = 1/2 × b × h

A = 1/2 × 6 × 8

A = 24 sq. cm

Thus the area of the triangle is 24 sq. cm.

**Example 2.**

What is the area of triangle and parallelogram if the base is 7 in and height 8 in?

**Solution:**

Given,

base = 7 in.

height = 8 in.

We know that,

Area of triangle = 1/2 × b × h

A = 1/2 × 7 × 8

A = 14 sq. in

Thus the area of the triangle is 14 sq. inches.

We know that,

Area of parallelogram = bh

A = 7 × 8

A = 56 sq. in

Thus the area of a parallelogram is 56 sq. inches.

**Example 3.**

If the area of a parallelogram is 49 sq. meters and height is 7 meters. Find the base of the parallelogram?

**Solution:**

Given that,

The area of a parallelogram is 49 sq. meters and

height is 7 meters

We know that,

Area of parallelogram = bh

49 = b × 7

b = 49/7

b = 7

Thus the base of the parallelogram is 7 meters.

**Example 4.**

What is the area of triangle and parallelogram if the base is 10 in and height 9 in?

**Solution:**

Given,

base = 10 in.

height = 9 in.

We know that,

Area of triangle = 1/2 × b × h

A = 1/2 × 10 × 9

A = 45 sq. in

Thus the area of the triangle is 45 sq. inches.

We know that,

Area of parallelogram = bh

A = 10 × 9

A = 90 sq. in

Thus the area of a parallelogram is 90 sq. inches.

**Example 5.**

Find the height of the triangle where the area is 100 sq. cm and the base is 50 cm?

**Solution:**

Given that,

the area is 100 sq. cm and

the base is 50 cm

We know that,

Area of triangle = 1/2 × b × h

100 = 1/2 × 50 × h

100 = 25 h

h = 100/25

h = 4

Thus the height of the triangle is 4 cm.

**Example 6.**

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 6cm, 8cm, and 10cm and the parallelogram stands on the base 8cm, find the height of the parallelogram?

**Solution:**

Perimeter of a triangle 2s = 6 + 8 + 10

2s = 24

s = 12

Area = √s(s – a)(s – b)(s – c)

Area = √12(12 – 6)(12 – 8)(12 – 10)

Area = 166

Area of Parallelogram = area of triangle

h × 8 = 166

h = 40.75

Height of the parallelogram is 40.75

Therefore h is 40.75 cm.

**Example 7.**

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 16cm, 18cm, and 20cm and the parallelogram stands on the base 18cm, find the height of the parallelogram?

**Solution:**

Perimeter of a triangle 2s = 16 + 18 + 20

2s = 54

s = 27

Area = √s(s – a)(s – b)(s – c)

Area = √27(27 – 16)(27 – 18)(27 – 20)

Area = 3600

Area of Parallelogram = area of triangle

h × 18 = 3600

h = 200

Height of the parallelogram is 200

Thus the height of the parallelogram is 200 cm.

**Example 8.**

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 24cm, 26cm, and 28cm, and the parallelogram stands on the base of 26. Find the height of the parallelogram?

**Solution:**

Area of the parallelogram = Area of the triangle

By using the area of parallelograms we can calculate the height of the parallelogram

Area of triangle = √s(s – a)(s – b)(s – c)

a, b, c are the sides of a triangle

S is the semi perimeter= half of the perimeter of the triangle

Let ABCD is a parallelogram and ABE is a triangle having a common base with parallelogram ABCD.

From ∆ABE

a = 28cm, b = 24cm, and c = 26cm

Semi perimeter (s) = perimeter/2

s = a + b + c/2

= 28 + 24 + 26/2 = 39

area of ∆ABE = √s(s – a)(s – b)(s – c)

√39(39 – 28)(39 – 24)(39 – 26)

= 289.23

Area of parallelogram ABCD = area of ∆ABE

Base × height = 289.23cm²

26cm² × height = 289.23cm²

Height = 11.12cm²

Thus the Height of the parallelogram is 11.12cm²

**Example 9.**

In the figure, ABCD is a Parallelogram N is a point BC such that BN: NC = 1: 4, DN produced meets AB produced at O. If the area of the triangle CNO = 40cm². Calculate the areas of the parallelogram ABCD and ∆CDN?

**Solution:**

Draw OP //BC which cuts DC produced at P.

Then CPOB is a parallelogram join CO.

Area of ∆BNO/∆CNO = BN/ND (both triangles have equal altitudes)

Area of ∆BNO/40cm² = 1/4

Area of (∆BNO) = 10cm²

Therefore

Area of (∆BCO) = area of ∆BNO + area of ∆CNO

= 10cm² + 40cm²

= 50cm²

Therefore

Area of parallelogram CDPO = 2area of ∆BCO = 2 × 50 cm² = 100cm²

Now

Area of parallelogram ABCD/area of parallelogram BCPO = base DC × height/ base CP × height

DC/CP (both the parallelograms have the same height)

Therefore

Area of parallelogram ABCD/area of parallelogram BCPO = DC/BO

∆NBO and ∆NCD

∆NBO = ∆NCD and ∆BON = ∆NDC (BO // DC)

Therefore

∆ NBO ~ ∆NCD

Corresponding sides are proportional

So, NB/NC = BO/DC

Area of ABCD/Area of BCPO = NC/NB = 4/1

Area of parallelogram ABCD = 4 × 100cm² = 400cm²

Now, area of ∆CDO = ½ × area of parallelogram ABCD

= ¼ × 400cm²

100cm²

Area of ∆CDN = area (∆CDO) – are of CNO

= 100cm² – 40cm²

A = 60 cm²

Thus the area of the traingle CDN is 60 sq. cm

**Example 10.**

In the figure XQ//SY, PS //QR, XS//SYnqnd QY = 4cm. Find the area of ∆MSR and parallelogram PQRS?

**Solution:**

Area of ∆MSR = ½ × area of a rectangle of SR of height QY

= ½ × SR × QY

½ × 6 × 4cm²

= 8cm²

Area of ∆MSR = ½ × area of parallelogram PQRS

Therefore

9cm² = ½ × area of parallelogram PQRS

Thus the Area of parallelogram PQRS = 8 × 2cm² = 16cm²

**Example 11.**

The angle between any two sides of a parallelogram is 60 degrees. If the length of the two parallel sides is 4cm and 6cm respectively then find the area.

**Solution:**

Let a = 4cm and b = 6cm

x = 60 degrees

Area = ab sin(90)

Area = 24 sin90

Area = 24 × 1 = 24 square cm

**Example 12.**

Find the area of the parallelogram with the base of 2cm and the height of 6cm.

**Solution:**

Given that

Base = 2cm, height = 6cm

We know that

Area of parallelogram = base × height square units

= 2 × 6 = 12cm

Therefore the area of parallelogram = 12cm²

**Example 13.**

The base of the parallelogram is twice its height. If the area is 182 cm². Find the base and height.

**Solution:**

Let the height of the parallelogram = h cm

Then the base of the parallelogram = 3h cm

Area of parallelogram = 182cm²

Area of Parallelogram = base × height

Therefore 182 = 3h × h

3 × h² = 182

h² = 182/3

Hence the height of the Parallelogram is 182/3 cm and breadth is

Breadth = 3 × h

= 3 × 182/3

= 182cm

**Example 14.**

The area of a parallelogram is 400 square cm. Its height is twice its base. Find the height and base.

**Solution:**

Given that

Area = 400 square cm

Height = twice of base

h = 2b

We know that

Area = breadth × height

400 = breadth × 2b

2b² = 400

b² = 200

b = 14.1

Height = 2 × b = 2 × 14.1 = 28.2cm

**Example 15.**

Find the area of Parallelogram whose breadth is 4cm and height is 2cm.

**Solution:**

Given that

Breadth = 4cm

Height = 2cm

Area of Parallelogram = breadth × height

= 4 × 2cm²

= 8cm²