6th Standard Syllabus & Materials
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Published on: 11/10/2019
Perimeter and Area
Download Tamil Nadu 6th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Your garden is in the shape of a square of side 5 m. Each side is to be fenced with 2 rows of wire. Find how much amount is needed to fence the garden at Rs. 10 per metre.
2.
The length of a rectangular park is 14 m more than its breadth. If the perimeter of the park is 200 m, what is its length? Find the area of the park.
3.
A piece of wire is 36 cm long. What will be the length of each side if we form
i) a square
ii) an equilateral triangle.
4.
Fill in the blanks.
i) 5 cm2 = _____ mm2
ii) 26 m2 = _____ cm2
iii) 8 km2 = _____ m2
5.
Four identical square floor mats of side 15 cm are joined together to form either a rectangular mat or a square mat. Which mat will have a larger area and a longer perimeter?
6.
Find the perimeter of the given figure.
7.
Find the side of the equilateral triangle of perimeter 129 cm.
8.
Find the cost of fencing a square plot of side 12 m at the rate of Rs. 15 per metre
9.
Find the perimeter of a triangle whose sides are 3 cm, 4 cm and 5 cm
10.
If the length of a rectangle is 12 cm and the breadth is 10 cm, then find its perimeter
11.
(i) Find the breadth of the rectangle with perimeter 14m and length 4m
(ii) The perimeter of an isosceles triangle is 21 cm. Find the measure of equal sides given that the third side is 5 cm.
12.
A square of side 2 cm is joined with a rectangle of length 15 cm and breadth 10 cm. Find the perimeter of the combined shape.
13.
The scalene triangle has 40 cm as its perimeter and whose two sides are 13 cm and 15 cm, find the third side
14.
A square park has 40 m as its perimeter. What is the length of its side? Also find its area.
15.
The area of a rectangular shaped photo is 820 sq. cm. and its width is 20 cm. What is its length? Also find its perimeter
16.
Find the perimeter and the area of a right angled triangle whose sides are 6 feet, 8 feet and 10 feet.
17.
Find the perimeter and the area of the square whose side is 8 cm
18.
Find the perimeter and the area of the rectangle whose length is 6 m and breadth is 4 m.
19.
The length and breadth of a rectangular sheet of a paper are 15 cm and 12 cm respectively. A rectangular piece is cut from one of its corners. Which of the following statement is correct for the remaining sheet?
Perimeter remains the same but the area changes
Area remains the same but the perimeter changes
There will be a change in both area and perimeter
Both the area and perimeter remains the same
20.
The side of a square is 10 cm. If its side is tripled, then by how many times will its perimeter increase?
2 times
4 times
6 times
3 times
21.
If every side of a rectangle is doubled, then its area becomes _____ times
2
3
4
6
22.
If two identical rectangles of perimeter 30 cm are joined together, then the perimeter of the new shape will be
equal to 60 cm
less than 60 cm
greater than 60 cm
equal to 45 cm
23.
Look at the picture of the house given and find the total area of the shaded portion.
24.
A closed shape has 20 equal sides and one of its sides is 3 cm. Find its perimeter.
1.
Square of side (s) = 5 m
Perimeter = 4s
=4 (5)m = 20m
Also, Given, Each side is to be fenced with 2 rows of wire.
= 2 (20) = 40 m
1 m = Rs. 10
40 m = Rs. 10 \(\times\) 40
= Rs. 400/-
2.
The length of a rectangular park is 14
m more than its breadth
1 = b + 14m -------- (1)
Perimeter P = 200 m
2 (1+ b) = 200
2 (1+ 2b) = 200
2 (b + 14) + 2b = 200 [by (1)]
2b + 28 + 2b = 200
4b = 200-28
\(4b=172\Rightarrow b=\cfrac { 172 }{ 4 } =43\)
b = 43 m
1 = b + 14 m
= 43 m + 14 m = 57 m
1 = 57 m
Area = Ib sq. units
= ( 57 \(\times\) 43) m2
\(\therefore\) I = 57 m, A = 2451 m2
3.
Given length = 36 cm
(i) a square 4 s = \(36\Rightarrow s=\cfrac { 36 }{ 4 } =9\) cm
Each side of a square = 9 cm
(ii) an equilateral triangle 3s = \(36\Rightarrow s=\cfrac { 36 }{ 3 } =12\)
Each side of the triangle = 12 cm
4.
i) 5 cm2 = 500 mm2
ii) 26 m2 = 2,60,000 cm2
iii) 8 km2 = 80,00,000 m2
5.
Perimeter of a rectangle, P = 2 (l + b) units.
= 2 (60+15) cm = 150 cm.
Area of a rectangle, A = (l \(\times\) b) sq. units.
= 60 \(\times\) 15
= 900 sq. cm.
Perimeter of a square, P = (4 \(\times\) s) units
= (4 \(\times\) 30) cm = 120 cm
Area of a square, A = (s \(\times\) s) sq. units.
= 30 \(\times\) 30
= 900 sq. cm.
There is no change in their areas. But, the rectangular mat will have longer perimeter
6.
Perimeter = Total length of the boundary
= (6 + 2 + 10 + 3 + 2 + 1 + 3 + 4 + 2 + 6 + 9) cm
= 48 cm
7.
Perimeter of the equilateral triangle, P = 129
a + a + a = 129
3 \(\times\) a = 129
\(a={129\over3}\)
= 43 cm
The side of the equilateral triangle is 43 cm.
8.
Side of a square plot = 12 m
Perimeter of the square plot = (4 \(\times\) s) units
= 4 × 12 = 48m
Cost of fencing the plot at the rate of Rs. 15 per metre = 48 × 15 = Rs. 720
9.
a = 3 cm
b = 4 cm
c = 5 cm
P = (a + b + c) units
= 3 + 4 + 5 = 12 cm
Perimeter of the triangle is 12 cm.
10.
l = 12 cm
b = 10 cm
P = 2 (l + b) units
= 2(12 + 10)
= 2× 22
= 44 cm
Perimeter of the rectangle is 44 cm.
11.
(i)In rectangle, Perimeter = 14m
Length = 4m
Breadth =?
P = 2(I + b)
14 = 2(4 + b)
14 = 8 + 2b
14 - 8 = 2b
\(6=2b\Rightarrow b=\cfrac { 6 }{ 2 } =3\)
\(\therefore\) Breadth = 3m.
(ii) In isosceles triangle 2 sides are equal.
P = 21 cm, 3rd side = 5 cm.
P = side 1 + side 2 + side 3
21 = (a + b + c)
21 = (a + a + 5)
\(21a=2a+5\Rightarrow 2a=21-5\)
2a = 16
\(2=\cfrac { 16 }{ 2 } =8\)
\(\therefore\) Equal sides = a = 3 cm, b = 8 cm.
12.
A square of side = 2 cm
A rectangle of length = 15 cm
and
breadth= 10 cm
Perimeter of the combined shape = Perimeter of square + Perimeter of rectangle.
Perimeter of the combined shape = 10 cm + 15 cm + 10 cm + 2 cm + 2 cm + 2 cm + 13 cm
\(\therefore\) P = 54 cm.
13.
Perimeter = 40 cm
Two sides are 13 cm and 15 cm
To find: 3rd side (c)
a + b + C = 40 \(\Rightarrow\) 13 + 15 + c = 40
\(\Rightarrow\) 28 +c = 40
c = 40 - 28 = 12cm
\(\therefore\) Third side = 12 cm
14.
Perimeter (P) = 40 m
Side (8) =?
Area (A) =?
4S = P
\(4S=40\Rightarrow S=\cfrac { 40 }{ 4 } =10m\)
A = S2 = 102 = 100m2
\(\therefore\) Side (S) = 10 m, Area (A) = 100 m2
15.
Area of a rectangle = 820 sq. cm
Width (b) = 20 cm
Length (l) =?
Perimeter =?
\(I=\cfrac { A }{ b } \)
= \(\cfrac { 820 }{ 20 } =41\\ \)
= =2(41+20)
= 2 (61) = 122 cm
\(\therefore\) I = 41 cm , P = 122 cm
16.
Sides are = 6 feet, 8 feet and 10 feet
Perimeter = ( a + b + c) feet
= (6+8+10) = 24 feet.
Area = \(\cfrac { 1 }{ 2 } \)bh.sq.feet
= \(\cfrac { 1 }{ 2 } \times 6\times 8\)
= 3 \(\times\) 8 = 24 feet
\(\therefore\) P = 24 feet, A = 24 sq. feet
17.
Side of the Square (s) = 8 cm
P = 4s
P = 4 \(\times\) 8 = 32 cm
Area = S2
= 82 = 64 cm2
18.
Length (l) = 6 m
breadth (b) = 4 m
Perimeter of the rectangle (P) = 2 (1+b) units
= 2 (6 + 4)
= 2(10) = 20m
Area(A) = l\(\times\)b = (6 \(\times\) 4)m2
= 24m
\(\therefore\) P = 20 m, A = 24 m2
19.
(c)
There will be a change in both area and perimeter
20.
(d)
3 times
21.
(c)
4
22.
(b)
less than 60 cm
23.
Total area of the shaded portion = Area of square + 2 (Area of triangle) + Area of rectangle
Square: side = 6 cm
Triangles: Same Triangles \(\Rightarrow\)b = 3, h = 4
Rectangle : b = 6 cm, I = 9 cm
\(\therefore\)Total area = s2 + 2 (\(\cfrac { 1 }{ 2 } bh\) ) + lb
= 62 + 2 (\(\cfrac { 1 }{ 2 } \)\(\times\) 3 \(\times\) 24)+ 6 \(\times\) 9
= 36 + 12 + 54
= 102 cm2
24.
Each side of shape = 3 cm
\(\therefore\) 20 equal sides perimeter = 20
times 3cm
P = 20 \(\times\) 3 = 60 cm
\(\therefore\) P = 60 cm
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Tamilnadu Stateboard 6th Standard Subjects
Tamilnadu Stateboard Standards
