Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Chapter 9: Perimeter and Area

    Introduction

    Area of a Parallelogram

    Area of a Triangle

    Circles

    Area of Circle

    Exercise 9.1

    Exercise 9.2

    What Have We Discussed ?

    Extra Curriculum Support

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Chapter 9: Perimeter and Area > Exercise 9.1

Exercise 9.1

1. Find the area of each of the following parallelograms.

(a)

(a) Base of parallelogram = cm
Height of parallelogram = cm
Area of a parallelogram = Base × Height = × = cm2

(b)

(b) Base of parallelogram = cm
Height of parallelogram = cm
Area of a parallelogram = Base × Height = × = cm2

(c)

(c)Base of parallelogram = cm
Height of parallelogram = cm
Area of a parallelogram = Base × Height = × = cm2

(d)

(d)Base of parallelogram = cm
Height of parallelogram = cm
Area of a parallelogram = Base × Height = × = cm2

(e)

(e)Base of parallelogram = cm
Height of parallelogram = cm
Area of a parallelogram = Base × Height = × = cm2

Find the area of each of the following triangles.

(a)

(a)Base of triangle = cm
Height of triangle = cm
Area of triangle = 12 × Base × Height = 12 × 4cm × 3cm = cm2

(b)

(b)Base of triangle = cm
Height of triangle = cm
Area of triangle = 12 × Base × Height = 12 × 5cm × 3.2cm = cm2

(c)

(c)Base of triangle = cm
Height of triangle = cm
Area of triangle = 12 × Base × Height = 12 × 3cm × 4cm = cm2

(d)

(d)Base of triangle = cm
Height of triangle = cm
Area of triangle = 12 × Base × Height = 12 × 3cm × 2cm = cm2
  • Fill in the blanks for the given area of parallelograms
S.NoBaseHeightArea of Parallelograms
(a)20 cm cm246 cm2
(b) cm15 cm154.5 cm2
(c) cm8.4 cm48.72 cm2
(d)15.6 cm cm16.38 cm2

Solution: Using the area of parallelogram formula: Area of parallelogram = base × height

(a) Height = AreaBase = 24620 = cm

(b) Base = AreaHeight = 154.515 = cm

(c) Base = AreaHeight = 48.728.4 = cm

(d) Height = AreaBase = 16.3815.6 = cm
  • Fill in the blanks for the given area of triangles
S.NoBaseHeightArea of Triangle
(a)15 cm cm87 cm2
(b) mm31.4 mm1256 mm2
(c)22 cm cm170.5 cm2

Solution: Using the area of triangle formula: Area of triangle = 12 base × height

(a) Height = 2×AreaBase = 2×8715 = cm

(b) Base = 2×AreaHeight = 2×125631.4 = mm

(c) Height = 2×AreaBase = 2×170.522 = cm

PQRS is a parallelogram Fig. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm.

Find: (a) the area of the parallegram PQRS

(a) SR = cm and QM = cm
Area of parallelogram PQRS = Base × Height
Area of parallelogram PQRS= SR × QM = × = cm2

(b) QN, if PS = 8 cm

(b) Base = PS = cm
Area of the parallelogram = cm2 [calculated in part(a)]
Area of parallelogram PQRS = Base × Height
91.2 cm2 = 8 cm ×
QN = = cm

In parallelogram ABCD, DL and BM are the heights on the sides AB and AD, respectively. If the area of the parallelogram is 1470 cm2, with sides AB = 35 cm and AD = 49 cm, find the length of BM and DL.

Finding BM and DL

  • From the fig., we know that parallelogram has area = cm2 and the side length values.
  • To find BM, we need to take as base which has a value of cm
  • We can write: cm2 = where BM = h
  • We get, BM = h = cm
  • Similarly, to find DL we take as base which has a value of cm
  • We can write: cm2 = where DL = y
  • We get DL = y = cm
  • BM and DL values have been found

∆ABC is right angled at A (shown below). AD is perpendicular to the side BC. If the length of the sides are: AB = 5 cm, BC = 13 cm and AC = 12 cm, find the area of ∆ABC. Also find the length of AD

Instruction

Finding Area and AD length

  • From the figure, we can see that the sides: acts as height and acts as base for the triangle (both are interchangeable)
  • Thus, the area is equal to cm2
  • Using this area to find, AD where we have acting as base.
  • cm2 = where length of AD is s.
  • Simplifying
  • Calculating i.e. s = cm
  • Value of height AD

∆ABC is an isosceles triangle with AB = AC = 7.5 cm and BC = 9 cm. The height AD, from A to BC is 6 cm. What is the area of ∆ABC. Also find the height from C to AB i.e. CE?

Instruction

Finding Area and height CE

  • From the figure, we can see that the area of the traingle can be sound using as height and as base.
  • Thus, the area is equal to cm2
  • Using this area to find CE where we have acting as base (equal to cm).
  • cm2 = where length of CE is h.
  • Simplifying
  • Calculating i.e. h = cm
  • Value of height CE