Introduction to 4th grade geometry problems

In general, 4th grade geometry problems includes types of polygons, area and perimeter of the polygons. Here we are going to see about  4th grade geometry problems on area and perimeter.  Area (A) is a two-dimensional measure. The area is measured in terms of square units such as square inches, square feet and square centimeters. Hectares and acres are also considered in some special cases. The entire boundary of a figure or the distance around the figure is called as the perimeter. For circle it is called as the circumference, such lengths are measured with inches, feet, and centimeters.

4th Grade Geometry Problems in Square:

Formula to find area and perimeter:

Area of square = side x side square unit.

Area of square (A) = a^2 square units,   (a is the side length of the square)

Perimeter of the square = 4 x side length.

Perimeter of the square (P)=4 x a.

1. Find the area and perimeter of the square, whose side length is 5 meters.

Sol:

Area of square =a^2

= 5 x 5

Area of square =25m^2

Perimeter of the square = 4 x a

=4 x 5

Perimeter of the square  = 20 meters

2. Find the area and perimeter of the square, whose side length is 12 feet.

Sol:

Area of square   =a^2

= 12 x 12

Area of square  =144ft^2

Perimeter of the square    = 4 x a

=4 x 12

Perimeter of the square = 48 feet ft.

4th grade geometry problems in Rectangle:

Formula to find the Area and perimeter of the rectangle:

Area of the rectangle (A) = length x width

Area (A) = l x  w (l is the length and w is the width of the rectangle )

perimeter of the rectangle = 2(length + width)

perimeter (p) =2(l x w)

1. Find the area and perimeter of rectangle, whose length and width are 12meter and 6 meter respectively.

Sol:

Area of rectangle = l x w  square unit.

Given:    Length= 12 meters, Width =6 meters

=12x6

Area of rectangle  = 72 m^2                

Perimeter of the rectangle   = 2(l + w)

=2(12 + 6)

= 2 (18)

Perimeter of the rectangle  = 36 meter

2. Find the area and perimeter of rectangle, whose length and width are 8.5meter and 3 meter respectively.

Sol:

Given: Length= 8.5 meters, Width =3 meters

Area of rectangle   = l x w square unit.

=8.5x3

Area of rectangle = 25.5m^2                

Perimeter of the rectangle    = 2(l + w)

=2(8.5 + 3)

= 2 (11.5)

Perimeter of the rectangle = 23 meter

4th Grage Geometry Problems in Circle:

Formula to find the area and circumference of the circle:

Area of the circle = πr^2

( r is the radius of the circle)

Circumference of the circle = 2πr


1. The radius(r) of a circle is 5 inches. Find the area and circumference of that circle?

Sol:

Given: r = 5inches

Area of the circle= π x r^2

π = 3.14

A = 3.14 x (5)^2

=3.14 x 25 inch^2.

Area  = 78.5 in^2

Circumference of the circle = 2πr.

π=3.14, r = 5 inches

Circumference of the circle = 2 x 3.14 x 5

= 31.4 inches


2. The radius(r) of a circle is 7 inches. Find the area and circumference of that circle?

Sol:

Area of the circle= π x r^2

Given:  r= 7inches,            

value of π=3.14

Area = 3.14 x (7)^2

= 3.14 x 49 inch^2.

Area  =  153.86 in^2

Circumference of the circle = 2πr.

π=3.14 , Given r = 7 inches

=2 x 3.14 x 7

Circumference of the circle = 43.96inches

Introduction to Word Problems based on Ratio and Proportion

A ratio is the comparison of two quantities by division. It is a relation that one quantity bears to another with respect to magnitude. If A and B are two numbers, than the ratio of A to B is A/B and is denoted by A:B. The ratio does not have any unit.

The equality of two ratios is called Proportion. If (A/B) = (C/D) , then A,B,C,D are said to be in proportion and can be written as

A : B :: C:D

The Ratio and Proportion world problems are a kind of problems in which , the relation between different quantity has to be determined and then using the definition of ratio and proportion, the unknown has to be calculated.

Here are some of the ratio and proportion word problems:

Ratio and Proportion: Word Problems.

Problem: Find the value of k that must be added to 7, 16, 43, 79 so that they are in proportion. (Answer: 5)

Problem: Find the fourth proportional to the numbers 60, 48, 30. (Answer: 24)

Problem: The Income of Alex and Bob are in the ratio of 3:2 and their expenditure in the ratio of 5:3. Find the income of Alex if each saves dollars 1000. (Answer:  $6000)

Problem: A mixture contains alcohol and water in the ratio of 12:5. On adding 14 litres of water, the ratio of alcohol to water becomes 1:1. Find the quantity of alcohol in the mixture. (Answer: 24 litres)

Ratio and Proportion: Multiple Choice Word Problems:

Problem 1: If the ratio of ages of Alex and Bob is 6:5 at present and fifteen years from now, the ratio will get changed to 9:8, then find Alex's age.

(A). 24 years

(B) 30 years

(C) 18 years

(D) 33 years

(Answer: (B) 30 years)

Problem 2: If dollars 58 is divided among 150 children such that each girl and each boy gets 25 dollars and 50 dollars respectively. Then how many girls are?

(A) 52

(B) 54

(C) 68

(D) 62

(Answer: (C) 68)

Problem 3: The number that must be added to each of the numbers 8, 21, 13 and 31 to make the ratio of first two numbers equal to the ratio of last two numbers is

(A) 5

(B) 7

(C) 9

(D) None of these.

(Answer: (A) 5)