## Picture problems:-

### Today in this article I will explain on picture problems which is actually based on mathematics problems and we will learn how to solve a picture problem of mathematics from a given picture,Hope these problems will help school going children a lot. Let's start,

## Question (i):-Find the area of the Yellow shaded region of the picture.

### Solution:

### ∵The above picture is made of a rectangle and a semi circle.

### To find:-The area of the Yellow

### shaded region of the picture ?

### In case, of semi circle

Radius of semi circle (r) = 7cm

∴ Area of the semi circle = ½ πr²

= (½ × 22/7×7×7)

[Let us assume,π=22/7]

= (11×7)

=77 cm²

Now,

In case,of rectangle,

length of the rectangle(l) = 2×r

= ( 2×7)

= 14 cm

breadth of the rectangle(b) = 9cm

∴ Area of the rectangle = l×b

= 14 × 9

= 126cm²

∴ Area of the yellow shaded region = Area of the rectangle - Area of the semi circle

= (126 -77)cm²

= 49cm²

## Question(ii) Find the area of the green shaded region of the picture.

### Solution:

### ∵The above picture is made of a rectangle and a square.

To find:-The area of green shaded region of the picture = ?

Solution:-

In case,of rectangle,

length(l) = 15m

breadth(b) = 10m

v∴ Area of the rectangle = l×b

= 15 × 10

= 150m²

In case of square,

Each side of the square (a) =7m

∴ Area of the square = a²

= (7 × 7)m²

= 49m²

∴ The area of green shaded region of the picture = Area of the rectangle - Area of the square

= (150 -49)m²

= 101m²

## Question(iii) FInd the area of the red shaded region of the picture.

### ∵The above picture is made of two circles.

To find:-The area of red shaded region of the picture = ?

Solution: 1st method:-

∵ The radius of bigger circle(R)= 14cm

∴ area of the bigger circle = πR²

= 22/7×14×14

= 22×2×14

= 22×28

= 616 cm²

∵ The radius of smaller circle(r)= 7cm

###

∴ area of the smaller circle = πr²

= 22/7×7×7[assuming, π=22/7]

=22×7

= 154cm²

∴ The area of red shaded region of the picture = (616-154)

= 462cm²

###

2ndmethod:-

∵ The radius of bigger circle(R)= 14cm

∵ The radius of smaller circle(r)= 7cm

∴The area of red shaded region of the picture = π(R²-r²)

= 22/7(14² - 7²)[Assuming π=22/7)

= 22/7(14+7)(14-7)[Applying identity, (a²- b²)= (a+b)(a-b)]

=(22/7× 21 ×7)

=(22×21)

=462cm²

## Question(iv) Find the area of the orange shaded region of the picture.

### ∵The above picture is made of a trapezium and a circle.

To find:-The area of orange shaded region of the picture = ?

Solution:-

In case of trapezium,

1st parallel side(a)= 10cm

2nd parallel side (b) = 16 cm

height of the trapezium(h) = 10 cm

∴ Area of the trapezium = ½ ×h (a+b)

=½ × 10(10+16)

= 5 × 26

= 130 cm²

In case of circle,

Radius of the circle (r) = 3.5 cm

∴ Area of the circle = πr²

= (22/7×3.5×3.5)cm²

=(22×.5 ×3.5)cm²

=11.0 × 3.5 cm²

= 38.5cm²

∴The area of orange shaded region of the picture = Area of the trapezium -Area of the circle

= (130-38.5)cm²

= 91.5cm²

## Question(v) The length of the side of a rhombus is 13cm and its one of diagonal is 24cm, find the area of the rhombus.

### . Solution:-

### ∵ Each side of the rhombus=AB=BC=CD=AD=13cm[∵All sides of a rhombus are equal]

It's longer diagonal(AC)=24cm and BD⊥AC

∵ Diagonals of a rhombus bisect each-othe perpandicularly.

∴AO =OC=½ AC = ½ ×24 cm

= 12cm

Now in right angled triangle AOD we get,

∵ OD²=AD²-AO²[∵<AOD =90°]

## FREQUENTLY ASKED QUESTIONS:-
## What is the area formula of a circle?

Answer:-The area formula of a circle is = πr², where r= radius of the circle.

## What is the area formula of a parallelogram?

Answer :- The area formula of a parallelogram = b × h, where b =Base of the parallelogram and h = height of the parallelogram.

## What is total surface area formula of a sphere?

Answer :- Total surface area formula of a sphere = 4πr²
where, r = Radius of the sphere

## What is total surface area formula of a hemi sphere ?

Answer :- The total surface area formula of a hemi sphere = 3πr²
where,r = Radius of the sphere.

##
What is the curved surface area of a cone ?

Answer :- The curved surface area of a cone = π rl
where, r = Radius of the cone,and l = slent height of the cone.

## What is the area formula of a circle?

Answer:-The area formula of a circle is = πr², where r= radius of the circle.

## What is the area formula of a parallelogram?

Answer :- The area formula of a parallelogram = b × h, where b =Base of the parallelogram and h = height of the parallelogram.

## What is total surface area formula of a sphere?

Answer :- Total surface area formula of a sphere = 4πr² where, r = Radius of the sphere

## What is total surface area formula of a hemi sphere ?

Answer :- The total surface area formula of a hemi sphere = 3πr² where,r = Radius of the sphere.

## What is the curved surface area of a cone ?

Answer :- The curved surface area of a cone = π rl where, r = Radius of the cone,and l = slent height of the cone.

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