KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2

KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 8 Heron’s Formula Exercise 8.2.

Karnataka Board Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2

Question 1.
A park, in the shape of a quadrilateral ABCD, has ∠C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
Solution:
BD is joined.
In Right angled ABCD, ∠C = 90°
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 1
As per Pythagoras Theorem,
BD2 = BC2 + CD2
= (12)2 + (5)2
= 144 + 25
BD2 = 169
∴ BD = 13m.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 2
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 3
Now, in ∆ABD,
Let a = 9m, b = 8m, c = 13m.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 4
∴ Area of quadrilateral ABCD,
= Area(∆ABD) + Area (∆BCD)
= 35.46 + 30
= 65.46 sq.m.
Area of quadrilateral ABCD = 65.46 sq.m.

Question 2.
Find the area of a quadrilateral ABCD which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 5
Solution:
In quadrilateral ABCD, AC is the diagonal.
In ∆ABC, a = 5cm, b = 3 cm, c = 4 cm.
∴ Perimeter = a + b + c = 5 + 3 + 4 = 12 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 6
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 7
∴ Area(∆ABC) = 6 sq. cm.
In ∆ADC, a1 = 5cm, b1 = 5 cm, c1 = 4cm.
∴ Perimeter = a1 + b1 + c1
= 5 + 5 + 4 = 14 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 8
Area of ∆ADC = 9.16 sq.cm.
∴ Area of quadrilateral aBCD,
= Area(∆ABC) + Area(∆ADC)
= 6 + 9.16
= 15.16 sq. cm.

Question 3.
Radha made a picture of an aeroplane with coloured paper as shows in Fig. Find the total area of the paper used.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 9
Solution:
(I) ∆ABC is an isosceles triangle.
AB = AC = 5 cm, and BC = 1 cm.
∴ a = 5 cm, b = 5 cm, c = 1 cm.
∴ Perimeter = a + b + c = 5 + 5 + 1 = 11 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 10
∴ Area(∆ABC) = 24.85 sq. cm.

(II) PBCS is a rectangle.
l = 6.5 cm, b = 1 cm.
Area of rectangle PBCS = l x× b
= 6.5 × 1 = 6.5 sq.cm.

(III) PQRS is a trapezium PT ⊥ QR
In Right angle ∆PTV,
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 11

(IV) Area of ADBE = Area of ∆FCG

(V)
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 12
∴ The total area of the paper used to make an aeroplane
= 2.485 + 6.5 + 1.29 + 4.5 + 4.5
= 19.275 sq. cm.

Question 4.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 13
Solution:
Perimeter of ∆ABC = 26 + 28 + 30 = 84 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 14

Question 5.
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting ?
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 15
Solution:
ABCD is a rhombus.
Area(∆ABD) = Area(∆BDC).
In ∆ABD, a = 30 m, b = 30 m, c = 48 m.
∴ Perimeter= a + b + c = 30 + 30 + 48 = 108 m
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 16
But, Area of whole field = 2 × area of ∆ABD
= 2 × 432
= 864 sq.m.
∴ Are required for growing grass for 18 cows is 864 sq.m.
∴ Area required for growing grass for 1 cow ………. ??
\(\frac{864}{18}\) = 48 sq.m.

Question 6.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 17
Solution:
Each sides of triangular shaped cloth
Let a = 50 cm, b = 50 cm, c = 20 cm.
∴ Perimeter = a + b + c
= 50 + 50 + 20 = 120 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 18
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 19
∴ Total Area of Umbrella mad up with 10 triangular shaped cloth is
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 20

Question 7.
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. How much paper of each shade has been used in it ?
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 21
Solution:
Kite is in the shape of square.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 22
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 23
∴ Total area = I + II + III
= 256 + 256 + 17.92
= 549.92 sq.cm.

Question 8.
A floral design of a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50p per cm2.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 24
Solution:
In the given figure there are 16 triangles.
Each sides of triangle are
a = 28 cm, b = 9 cm, c = 35 cm.
Perimeter of triangle = a + b + c
= 28 + 9 + 35 = 72 cm.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 25
∴ Area of 16 triangles = 16 × 88.2 = 1411.2 sq.cm.
Polish expenditure for 1 sq.cm. = 50 p = Re. 0.5.
∴ Polish expenditure for 1411.2sq. cm. =?
= 1411.2 × 0.5
= Rs 705.6

Question 9.
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 26
Solution:
ABCD is a trapezium.
AB || DC.
Draw AE || BC and AF ⊥ DC.
∴ ABCE is a parallelogram.
DE = DC – EC = 25 – 10
DE = 15 cm.
Sides of ∆ADE
a = 14 cm, b = 13 cm. c = 15 cm.
∴ Perimeter= a + b + c
= 14 + 13 + 15 = 42 cm.
∴ s = \(\frac{a+b+c}{2}=\frac{42}{2}=21 \mathrm{cm}\)
∴ Area of ∆ADE, A
KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 27

(ii) Area of quadrilateral ABCE = base × height
= EC × AF
= 10 × 11.2
= 112.0
= 112 sq.cm.
∴ Complete area of trapezium ABCD, A
A = Area of ∆ADE + Area of quadrilateral ABCE
= 84 + 112
= 196 sq.cm.

We hope the KSEEB Solutions for Class 9 Maths Chapter 8 Heron’s Formula Ex 8.2 help you. If you have any query regarding Karnataka Board Class 9 Maths Chapter 8 Heron’s Formula Exercise 8.2, drop a comment below and we will get back to you at the earliest.

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