Heron`s Formula Test

Result

Heron`s Formula Test - 1

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Question 1
1 / -0

In a quadrilateral ABCD, AB = 10 cm, BC = 12 cm, CD = 7 cm, AD = 9 cm and diagonal AC = 14 cm. The area of ABC is

A
cm²

B
24cm²

C
12 cm²

D
8cm²

Solution

According to Heron's formula,

A =
P = Semi-perimeter
a, b and c are the sides of the triangle.

P of ABC =
Area = cm²
= cm²
=
= cm²
= 2 2 2 3cm²
=
Question 2
1 / -0

What is the area of the given triangle?

A
44 cm²

B
cm²

C
11 cm²

D
12 cm²

Solution

Let P be the semi-perimeter of the triangle.

P = cm

Area = unit²
Area = cm²
Area = cm²
= 2 x 2 x 3 cm²= 12 cm²
Question 3
1 / -0

ABC is an isosceles triangle with AB = AC = a cm. If BC = b cm, then use Heron's formula to find the area of the triangle.

A

B

C
(a - b)

D

Solution

s =

Area of triangle =
By solving, we get
Area of triangle =
Question 4
1 / -0

In a triangle ABC, AB = 6 cm, BC = 7 cm and AC = 9 cm. The area of ABC is

A
cm²

B
2cm²

C
4cm²

D
cm²

Solution

Let P be the semi-perimeter of the triangle.

P = cm
Area = unit²
Area = cm²
Area = cm²

= 2 cm²
Question 5
1 / -0

ABCD is a rhombus with AB = 6 cm and AC = 8 cm. What is the area of the rhombus?

A

B

C

D

Solution

ABCD is a rhombus.
AB = BC = CD = DA = 6 cm
AC = 8 cm
Area of rhombus = 2 x area of ABC
Now, area of ABC =
S =
Area of ABC =
= cm²
Area of rhombus = 2( Area of triangle ABC) = 16cm²
Question 6
1 / -0

XYZ has sides XY = 20 cm, YZ = 30 cm and XZ = 40 cm. What is the length of the altitude from vertex X?

A

B

C

D

Solution

S = cm
Area = cm²

=
Also,
Area =

Or height =
Question 7
1 / -0

What is the area of the given figure?

A
124 cm²

B
114 cm²

C
54 cm²

D
104 cm²

Solution

Area of triangle with sides 8 cm, 15 cm and 17 cm:

Semi perimeter = ( a + b + c) / 2 = ( 8 + 15 + 17) / 2 = 20 cm

Area by Heron's formula = =
= 3 4 5 = 60 cm²Area of triangle with sides 9 cm, 15 cm and 12 cm:

S =

= 54 cm²= 114 cm²
Question 8
1 / -0

An irregular octagon is formed by joining 8 triangles, each having dimensions 8 cm, 7 cm and 9 cm. What is the total area of the octagon?

A
96 cm²

B

C
84 cm²

D
72 cm²

Solution

Total area of the octagon = 8 times the area of triangle with sides 8 cm, 7 cm and 9 cm.
Area of triangle:
a = 8 cm, b = 7 cm, c = 9 cm =
Therefore, area =
Therefore, area of octagon =
= 96 cm²
Question 9
1 / -0

A showpiece is made up of three triangles measuring 4 cm, 5 cm and 7 cm. What is the total area of the showpiece?

A

B
cm²

C

D

Solution

Area of one triangle =
S =
Area of one triangle =
=
=
Total area of showpiece = 3
= 12cm²
Question 10
1 / -0

What is the area of an isosceles triangle whose sides measure a cm, a cm and b cm?

A
sq. cm

B
sq. cm

C
sq. cm

D
sq. cm

Solution

S = cm
S – a = cm
s – a = cm
s – b = cm
Area = sq. cm
= sq. cm
Question 11
1 / -0

In a triangle, the three sides a, b and c measure 9 cm, 6 cm and 5 cm, respectively. What is the length of the altitude to the side 'b' from the opposite vertex?

A

B

C

D

Solution

S = semi-perimeter =
Now,

Or height =
Question 12
1 / -0

ABC is a scalene triangle. If AB = 3 cm, BC = 6 cm and AC = 5 cm, what is the area of the triangle?

A

B

C

D

Solution

Let a = 3 cm
b = 5 cm
c = 6 cm

S =
S =
S =
Now, area of ABC =
=
=
=
Question 13
1 / -0

If the lengths of the sides of a triangle are doubled, then which of the following shows the correct relationship between the new area (A₂) and the old area (A₁)?

A
4A₂ = A₁

B
A₂ = A₁

C
A₂ = 4A₁

D
A₂ = 2A₁

Solution
Question 14
1 / -0

What is the area of the given triangle?

A

B

C

D

Solution

Let a = 11 cm
b = 7 cm
c = 10 cm
Then, S = cm
= cm
Area by Heron's formula =
=
=
=
Question 15
1 / -0

What is the area of a parallelogram with adjacent sides measuring 12 cm and 5 cm and the diagonal corresponding to the given two sides measuring 13 cm?

A
30 cm²

B
60 cm²

C

D

Solution

ABCD is a parallelogram.
AB = CD = 12 cm
and BC = AD = 5 cm
Area of parallelogram ABCD = 2 area of ABC
Now, S = cm
Area of ABC =
= cm²
= 30 cm²
Now, Area of parallelogram = 2 30 cm²
= 60 cm²