AP State Syllabus 8th Class Maths Solutions 9th Lesson Area of Plane Figures InText Questions

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions and Answers.

8th Class Maths 9th Lesson Area of Plane Figures InText Questions and Answers

Do this

Question 1.
Find the area of the following figures:     [Page No. 200]
i)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 1
Answer:
Area of a parallelogram = b × h = 7 × 4 = 28 sq.cm.

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

ii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 2
Answer:
Area of a triangle = \(\frac{1}{2}\) bh = \(\frac{1}{2}\) × 7 × 4
= 14 sq.cm.

iii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 3
Answer:
Area of a triangle = \(\frac{1}{2}\) bh = \(\frac{1}{2}\) × 5 × 4
= 10 sq.cm.

iv)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 4
Answer:
Area of rhombus = \(\frac{1}{2}\) d1d2
= \(\frac{1}{2}\) × (4+4) × (3+3)
[∴ d1 = 4 + 4 = 8, d2 = 3 + 3 = 6]
= \(\frac{1}{2}\) × 8 × 6
= 24 cm2

v)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 5
Answer:
Area of a rectangle = l × b
= 20 × 14 = 280 sq.cm

vi)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 6
Answer:
Area of a square = s2
= s × s
= 5 × 5 = 25 cm2

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

Question 2.
The measurements of some plane figures are given in the table below. However, they are incomplete. Find the missing information.     [Page No. 200]
Answer:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 7

Question 3.
Find the area of the following trapezium.      [Page No. 204]
fig (i)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 8
Answer:
Area of a trapezium
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 9
fig (ii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 10
Answer:
Area of a trapezium
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 11

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

Question 4.
Area of a trapezium is 16 cm2. Length of one parallel side is 5 cm and distance between two parallel sides is 4 cm. Find the length of the other parallel side. Try to draw this trapezium on a graph paper and check the area.
[Page No. 204]
Answer:
Given that
Area of a trapezium = 16 sq.cm
Length of one of the parallel sides is a = 5 cm; h = 4 cm
Length of 2nd parallel side (b) = ?
A = \(\frac{1}{2}\)h(a + b)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 12
Graph Sheet:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 13
Area of parallelogram ABCD = 12 sq.cm + (S + P) + (Q + R) + (W + T) + (V + U)
= 12 + 1 + 1 + 1 + 1
= 12 + 4
= 16 sq.cm

Question 5.
ABCD is a parallelogram whose area is 100 sq.cm. P is any point insile the parallelogram (see fig.) find tie area of △APB + △CPD.       [Page No. 204]
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 14
Answer:
Area of parallelogram ABCD = 100 sq.cm
From the given figure,
ar (△APB) + ar (△CPD) = ar (△PD) + ar (△BPC)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 15

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

Question 6.
The following details are noted in meters in the field book of a surveyor. Find the area of the fields.     [Page No. 213]
i)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 16
Answer:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 17
From the above figure
i) A, B, C, D, E are the vertices of pentagonal field,
ii) AD is the diagonal.
iii) Now the area of the field = Areas of 4 triangles and a trapezium.
PQ = AQ – AP = 50 – 30 = 20
QD = AD – AQ = 140 – 50 = 90
RD = AD – AR = 140 – 80 = 60
Area of △APB:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 18
Area of trapezium PBCQ:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 19
Area of △QCD:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 20
Area of △DER:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 21
Area of △ERA:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 22
∴ Area of the field = ar △APB + ar trapezium PBCQ + ar △QCD + ar △DER + ar △ERA
= 450 + 800 + 2250 + 1500 + 2000 = 7000 sq. units
ii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 23
Answer:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 24
From the above figure
i) A, B, C, D, E are the vertices of a pentagonal field.
ii) AC is the diagonal.
iii) The area of a field is equal to areas of 4 triangles and a trapezium.
QC = AC – AQ = 160 – 90 = 70
RC = AC – AR = 160 – 130 = 30
PR = AR – AP = 130 – 60 = 70
Area of △AQB:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 25
Area of △QBC :
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 26
Area of △DRC :
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 27
Area of trapezium EPRD:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 28
Area of △EPA :
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 29
∴ Area of the field = ar △AQB + ar △QBC + ar △DRC + ar trapezium EPRD + ar △EPA
= 2700 + 2100 + 450 + 2450 + 1200 = 8900 sq. units

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

Try these

Question 1.
We know that parallelogram is also a quadrilateral. Let us split such a quadrilateral into two triangles. Find their areas and subsequently that of the parallelogram. Does this process in turn with the formula that you already know?   [Page No. 209]
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 30
Answer:
Area of a parallelogram ABCD
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 31
Area of parallelogram ABCD
= base x height
= bh sq. units
(OR)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 32
Area of parallelogram ABCD
= ar △ABC + ar △ACD
= \(\frac{1}{2}\) BC × h1 + \(\frac{1}{2}\) AD × h2
= \(\frac{1}{2}\) bh + \(\frac{1}{2}\) bh [∵ h1 = h2]
= bh sq. units.
∴ This process in turn with already known formula.

Question 2.
Find the area of following quadrilaterals.      [Page No. 213]
i)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 33
Answer:
d = 6 cm, h1 = 3 cm, h2 = 5 cm
Area of a quadrilateral
= \(\frac{1}{2}\)d(h1 + h2)
= \(\frac{1}{2}\) × 6 (3 + 5) = 3(8) = 24 cm2

ii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 34
Answer:
d1 = 7 cm; d2 = 6 cm
Area of a rhombus A = \(\frac{1}{2}\) d1d2
= \(\frac{1}{2}\) × 7 × 6
= 7 × 3 = 21 cm2

iii)
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 35
Answer:
Area of a parallelogram (A) = bh
(∵ The given fig. is a parallelogram in which two opposite sides are parallel)
Area of a parallelogram = 2 ar AADC
= 2 × \(\frac{1}{2}\) × 8 × 2 = 16 Sq. cm.
[∵ Area of a parallelogram = ar △ADC + ar △ABC. But ar △ABC = ar △ADC]

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

Question 3.
i) Divide the following polygon into parts (triangles and trapezium) to find out its area.     [Page No. 214]
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 36
Answer:
FI is a diagonal of polygon EFGHI.
If perpendiculars GA, HB are drawn on the diagonal FI, then the given figure pentagon is divided into 4 parts.
∴ Area of a pentagon EFGHI = ar △AFG + ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 43AGHB + ar △BHI + ar △EFI.
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 37
NQ is a diagonal of polygon MNOPQR. Here the polygon is divided into two parts.
∴ Area of a hexagon MNOPQR = ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 44 NOPQ + ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 44 MNQR.

ii) Polygon ABCDE is divided into parts as shown in the figure. Find the area.     [Page No. 215].
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 38
If AD = 8 cm, AH = 6 cm, AF = 3 cm and perpendiculars BF = 2 cm, GH = 3 cm and EG = 2.5 cm.
Answer:
Area of polygon ABCDE = ar △AFB + ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 43FBCH + ar △HCD + ar △AED
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 39
So, the area of polygon ABCDE = 3 + 7.5 + 3 + 10 = 23.5 sq.cm

AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions

iii) Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2 cm.   [Page No. 215].
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 40
NA, OD, QC and RB are perpendiculars to diagonal MP.
Answer:
Area of MNOPQR
= ar △MAN + ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 43 ADON + ar △DOP + ar △CQP + ar AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 43 BCQR + ar △MBR
Hence CP = MP – MC = 9 – 6 = 3 cm
BC = MC – MB = 6 – 4 = 2 cm
AB = MB – MA = 4 – 2 = 2 cm
DP = MP – MD = 9 – 7 = 2 cm
AD = MD – MA = 7 – 2 = 5 cm
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 41
= 2.5 + (2.5 × 5.5) + 3 + 3 + 4.5 + (2 × 2.5)
= 2.5 + 13.75 + 3 + 3 + 4.5 + 5
= 31.75 sq.cms

Think, discuss and write

Question 1.
A parallelogram is divided into two congruent triangles by drawing a diagonal across it. Can we divide a trapezium into two congruent triangles?    [Page No. 213]
Answer:
AP Board 8th Class Maths Solutions Chapter 9 Area of Plane Figures InText Questions 42
No, we cannot divide a trapezium into two congruent triangles.
∵ From the adjacent figure,
△ABC ≆ △ADC