Trapezium area:-
Today in this article I will discuss on the topic trapezium area, hope this will help school going students a lot.To start my discussion, first I want to explain you,
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***What is Trapezium?
Answer:- A quadrilateral whose any two sides are parallel is termed as trapezium.
In the picture,
AB∥CD of the quadrilateral ABCD
So, ABCD is a trapezium.
***What is perimeter of a trapezium?
Answer:- The perimeter of a trapezium is total surrounding spaces covered by a trapezium,but in simple words we can say that sum of all four sides of a trapezium is its perimeter.
So, perimeter of a trapezium is = Sum of its all four sides.
Now, we will solve
**some problems based on perimeter of trapezium:-
(1) If four sides of a trapezium are 6cm,4cm,3cm and 5 cm, then find the perimeter of the trapezium?
Answer:- Here,
1st side of the trapezium(a)=6cm
2nd side of the trapezium(b)=4cm
3rd side of the trapezium(c)=3cm
and,
4th side of the trapezium(d)=5cm
∴Perimeter of the trapezium=a+b+c+d
=(6+4+3+5)cm
=18cm
(2)If three sides of a trapezium measures 5m,6m, 4m and the perimeter of the trapezium is 30m, then find fourth side of the trapezium.
Answer:- 1st method:-
Here,
Perimeter of the trapezium = 30m
1st side of the trapezium(a)=5m
2nd side of the trapezium(b)=6m
3rd side of the trapezium(c)=4m
Let , the 4th side of the trapezium= dm
Now, according to question,
a+b+c+d=30
=> 5+6+4+d=30
=>15+d=30
=>d=30-15
=>d=15
∴ The 4th side of the trapezium(d)=15m
2nd method:-
∵ Perimeter of the trapezium = 30m
and sum of its three sides =(5+6+4)cm
=15cm
let, the 4th side od the trapezium=d m
∴ 4th side of the trapezium(d)=(30-15)cm
=15 cm
Now I will discuss on ,
***What is trapezium area?
Answer:-
The area of a trapezium means total space occupied by a trapezium inside its sides i.e; all the inside space coverd by its four sides ,The formula of trapezium area is given by
Area of trapezium= ½ (a+b)×h
where,
a= 1st parallel side of the trapezium
b= 2nd parallel side of the trapezium
h= height of the trapezium
Some problems related on trapezium area:-
***(i) If two parallel sides of a trapezium are 4cm,6cm respectively and height is 3cm, find the area of the trapezium.
Answer:-
∵1st parallel side of the trapezium(a)= 4cm
and 2nd parallel side of the trapezium(b)=6cm
also height of the trapezium(h)= 3cm
∴ Area of the trapezium=½(a+b)×h
=½(4+6)×3cm²
=½×10×3cm²
=5×3 cm²
=15 cm²
***(ii) The area of a trapezium is 50 cm²,its height is 5cm, one parallel side is 6cm, find the other parallel side.
Answer:- The area of trapezium = 50 cm²
height of the trapezium(h)=5cm
one of its parallel side (a)= 6cm
Let, other parallel side = b cm
Now, according to question,
½×h(a+b) = 50
=>½× 5 (6+b) = 50
=>(6+b) =(50×2)÷5
=> 6+b =100/5
=> 6+b =20
=> b =20-6
=> b =14∴ Other parallel side of the trapezium(b)= 14cm
***(iii) From the given picture find the area of the shape.
Solution:- Given shape consists with two trapezium (at the top and at the bottom) and a rectangle in the middle.
In case of rectangular part,
Length of the rectangle(l)=50cm
breadth of the rectangle(b)=10cm
∴ Area of the rectangular part = l × b
=(50×10)cm²
=500 cm²
Again,
Incase of trapezium part,
1st parallel side of the trapezium(a)=30cm
2nd parallel side of the trapezium(b)=10cm
Height of the trapezium (h) =(70-50)cm
=20cm
∴ Area of trapezium part =½×h×(a+b)
=½ × 20×(30+10)
=(10×40) cm²
= 400 cm²
Now, The are of the given shape = 2×Area of the trapezium part +Area of rectangular part
= (2×400 + 500) cm²
=(800+500) cm²
= 1300cm²
****(iv)If two parallel sides of a trapezium are 5m and 3m also its area 30m² find the height of the trapezium. Answer:-
Here,
1st parallel side(a) of the trapezium=5m
2nd parallel side(b) of the trapezium=3m
Arra of the trapezium =30m²
Let, the height of the trapezium = h m
According to question,
FREQUENTLY ASKED QUESTIONS:-
What is area formula of a scalene triangle?
Answer:-The area formula of a scelene triangle = √s(s-a)(s-b)(s-c) where,s = half/semi perimeter of the triangle , and a b and c are its different sides.
What is rhombus area formula ?
Answer:- Rhombus area formula = 1/2 × d₁× d₂,where d₁ = 1st diagonal of the rhombus.and d₂ = 2nd diagonal of the rhombus.
What is circle area formula ?
Answer:- Circle area formula = πr², where r = Radius of the circle.
What is minor sector area formula of a circle ?
Answer:- The minor sector area formula of a circle = πr²θ/360°,Where r = radius of the circle and θ = angle subtended by the radius at center of the circle.
What is minor segment area formula of a circle?
Answer:- The minor segment area formula of a circle = 1/2 r²(πθ/360°- Sinθ)Where,r=radius of the circle,θ = angle subtended by the chord of the circle.
What is the area formula of a square?
.
Answer:- The area formula of a square = a² where, a = Each side of the square
What is area formula of a scalene triangle?
Answer:-The area formula of a scelene triangle = √s(s-a)(s-b)(s-c) where,s = half/semi perimeter of the triangle , and a b and c are its different sides.
What is rhombus area formula ?
Answer:- Rhombus area formula = 1/2 × d₁× d₂,where d₁ = 1st diagonal of the rhombus.and d₂ = 2nd diagonal of the rhombus.
What is circle area formula ?
Answer:- Circle area formula = πr², where r = Radius of the circle.
What is minor sector area formula of a circle ?
Answer:- The minor sector area formula of a circle = πr²θ/360°,Where r = radius of the circle and θ = angle subtended by the radius at center of the circle.
What is minor segment area formula of a circle?
Answer:- The minor segment area formula of a circle = 1/2 r²(πθ/360°- Sinθ)Where,r=radius of the circle,θ = angle subtended by the chord of the circle.
What is the area formula of a square?
. Answer:- The area formula of a square = a² where, a = Each side of the square
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