PROPERTIES OF SQUARE WORKSHEET

Problem 1 :

The square ABCD, find each length or angle measure.

Solution

Problem 2 :

Classify the special quadrilateral. Then find the values of x and y. 

Solution

Problem 3 :

For the square ABCD, find the missing values.

Solution

Problem 4 :

The diagonals of square DEFG intersect at H. Given that EH = 5, find the indicated measure. 

Solution

Problem 5 :

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the center as shown in figure given below. Find the area of shaded portion.

Solution

Problem 6 :

A large square is made by arranging a small square surrounded by four congruent rectangles as shown in figure given below. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.

Solution

Problem 7 :

ABCD is a square with AB = 15 cm. Find the area of the square BDFE. 

Solution

Problem 8 :

In the figure, ABCD is a square. If ∠DPC = 80°, then find the value of x.

Solution

Problem 9 :

In the figure ABCD is a square and CDE is an equilateral triangle. find 

(i) ∠AED      ii) ∠EAB      iii)  Reflex of ∠AEC

Solution

Problem 10 :

ABCD is a square, diagonal AC is joined. Then the measurement of ∠CAB is

(a) 35°       (b) 40°          (c) 45°          (d) 50°

Solution

Problem 11 :

Choose the most appropriate alternative for the given statement:

A square’s diagonals are _________ to each other.

a) Equal     b) Unequal      c) Parallel      d) None of the above

Solution

Problem 1 :

Find the area of a square with a diagonal of 3 cm.

Solution

Problem 2 :

Find the area of a square whose diagonal is 9 cm.

a) 18 cm²   b) 81/2 cm²     c) 36 cm²    d) 81 cm²

Solution

Problem 3 :

The area of a square is 2√2 + 3. What is the length of a side of the square?

a) √2 - 1    b) 2√2 - 1    c) √2 + 1    d) 2√2 + 1

Solution

Problem 4 :

The area of the square ABCD is 9/2 cm². Find the length of BD.

Solution

Problem 5 :

Find the area of a square one of whose diagonal is 3.8 m long.

Solution

Problem 6:

The diagonals of two squares are in the ratio 2 : 5. Find the ratio of their areas.

Solution

Problem 7 :

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

a) 20       b) 24       c) 30       d) 33

Solution

Problem 8 :

A man walking at the speed of 4 kmph crosses square field diagonally in 3 minutes. The area of the field is.

a) 18000 m²    b) 19000 m²  c) 20000 m²   d) 25000 m²

Solution

Problem 9 :

If the length of the diagonal of a square is 20 cm, then its perimeter must be

a) 10√2 cm      b) 40 cm    c) 40√2 cm     d) 200 cm

Solution

Problem 10 :

The area of a square field is 69696 cm². its diagonal will equal to.

a) 313.296 m      b) 353.596 m

c) 373.296 m      d) 393.296 m

Solution

Problem 11 :

The diagonal of a square measures 7√2 , what is its perimeter?

Solution

Problem 12 :

If the diagonal of a squares is made 1.5 times then the ratio of the area of the two squares is :

a) 4 : 3   b)  4 : 5   c)  4  7   d)  4 : 9

Solution

Problem 13 :

A man walking at the speed of 4 kmph crosses the square field diagonally in 3 minutes. The area of the field is 

a) 18000 m²       b) 19000 m²          c)  20000 m²     d) 25000 m²

Solution