# 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,

# Listen full article:

## ***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