Worksheet on Area and Perimeter of Triangle | Area and Perimeter of Triangles Word Problems Worksheet

Given sides of the triangle=4cm, 6cm, 8cm
The perimeter of the triangle=a+b+c where a,b, and c are the sides of the triangle.
The perimeter of the triangle=4 cm + 6 cm + 8 cm
=18 cm
Therefore, the perimeter of the triangle is 18 cm.
ii. Given sides of the triangle=7 cm, 9cm, 11cm
We know that the perimeter of the triangle=a+b+c where a,b, and c are the sides of the triangle.
The perimeter of the triangle=7 cm + 9 cm + 11 cm
=27 cm
Therefore, the perimeter of the triangle is 27 cm.

Given that,
The three sides of a triangle are in the ratio of 3:5:7.
Perimeter=345 m
Length of first side =3x
Length of second side =5x
Length of third side =7x
The perimeter of the triangle=side1+side2+side3
345 m=3x + 5x + 7x
345 m=15x
x=345 m/15=23 m
Length of first side=3x=3(23 m)=69 m
Length of the second side=5x=5(23 m)=115 m
Length of the third side=7x=7(23 m)=161 m
Area of the triangle=\(\sqrt{ s(s-a)(s-b)(s-c) }\)
S =perimeter of triangle /2 = 345 m/2 =172.5 m
=\(\sqrt{172.5(172.5-69)(172.5-115)(172.5-161) }\)
=\(\sqrt{172.5(103.5)(57.5)(11.5)  }\)
=\(\sqrt{11805792.1875 }\)
=3435.95 sq m
Therefore, Area of the triangle is 3435.95 sq m.

Given that,
Base=30 cm, Area=600 sq cm
We know that Area= 1/2 × b × h
600 sq cm=1/2 × 30 cm × h
h=600 × 2 /30
=1200/30
=40 cm
Therefore, the Height is 40 cm.

We know that area of the triangle=1/2 × b × h
=1/2 × 12 × 12
=72 sq cm
Therefore, the Area of an isosceles right-angled triangle is 72 sq cm.

Given that,
The area of the triangle is equal to the area of a square.
Side of a square=20 cm
Area of a square=side × side
=20 × 20=400 sq cm
Therefore, the Area of triangle=400 sq cm.
we know that area of triangle=1/2 × b × corresponding altitude
400=1/2 × b × 24
b=400/12
b=33.33
Therefore, the base of the triangle is 33.33 cm.

Given that,
sides of triangle are in ratio of 8:5:7
perimeter of triangle = 600
8x + 5x + 7x = 600
20x = 600
x = 600/20
x = 30
Therefore the sides are
8x = 8 × 30 = 240
5x = 5 × 30 = 150
7x = 7 × 30 = 210
Area of triangle with sides given we use herons formula
area = \(\sqrt{s(s-a)(s-b)(s-c)  }\)
s = (a+b+c)/2 where a, b, c are the sides of triangle
=(240+150+210)/2
=600/2=300
area=\(\sqrt{ 300(300 – 240)(300 – 150)(300 – 210) }\)
=\(\sqrt{300(60)(150)(90)}\)
=\(\sqrt{243000000}\)
=15588.45 sq cm
Altitude corresponding to smallest side is 150
15588.45=1/2 × 150 × h
h=31176.9/150
h=207.84 cm
Hence, height is 207.84 cm.

Given that,
The length of diagonal d=84m
The perpendicular distance of the other two vertices from the diagonal h1 = 15 m and
h2=12 m
We know that Area of the quadrilateral=1/2×d(h1+h2)
=1/2× 84(15+12)
=42(27)
=1134 sq m
Hence, the Area of the field is 1134 sq m.

Given that,
The perimeter of a triangle is= 68 cm
let X = first side
Y = second side
Z = third side
X = Y – 7 (1)
Z = 4X – 5 (2)
68 = X + Y + Z (3)
use (1) (2) into (3)
68 = ( Y – 7 ) + Y + ( 4X – 5 )
68 = Y – 7 + Y + 4X – 5
68 + 7 + 5 = 2Y + 4X
80 = 2(Y + 2X)
y+2x=40
y=40-2x– (4)
substitute (4) to (1)
X = (40 – 2X) – 7
X = 33 – 2X
3X = 33
X = 11 cm
length of first side
use X in (1)
11 = Y – 7 ; Y = 18 cm
use X in (2)
Z = 4(11) -5
Z =39 cm
Hence, x=11cm, y=18 cm,z=39 cm.

Let the height of a triangle = h
The base of a triangle = b
∴ The area of a triangle =1/2bh ……. (1)
The new height of a triangle = 3h
The new base of a triangle = 2b
The area of a new triangle=1/2(3h)(2b)
=6(1/2hb)
Using equation (1), we get
= 6 × The area of a triangle
Thus, the area of the triangle becomes “6 times”.

Given that,
Hypotenuse AC=5 cm
one of the side containing the right angle BC=3 cm
Let the other side AB be= x cm
By pythagerous theorem,
AC²=AB²+BC²
(x)²+(3)²= (5)²
(x)²+9=25
(x)²=25-9
x= 4 cm
Area of triangle= 1/2×3×4=6 sq cm.

The string length is the perimeter of the shape.
perimeter=60cm
An equilateral triangle has three equal sides.
Perimeter=3×(side)
∴side=perimeter/3
​=60/3
=20cm
Hence, the length of each side of the string is used to form an equilateral triangle will be 20 cm.
Area=\(\sqrt{ 3}\)a²/4
=\(\sqrt{ 3}\) (20)2/4
=\(\sqrt{ 3}\) 400/4
=100\(\sqrt{ 3}\) sq cm
Therefore, The area of an equilateral triangle is 100\(\sqrt{ 3}\) sq cm.