Question

# The parallel sides of a trapezium are 30 cm and 10 cm and the other two sides are 13 cm and 21 cm. Find its area?

Hint:

### Draw the parallel line from B parallel to AD which cuts the CD at E .

We get a triangle and parallelogram. we find the area of triangle in both heron's

method and using formula area = ½ b × h and equating we get height h

Now , find the area of Trapezium = ½ height × (sum of lengths of parallel sides).

## The correct answer is: 252 cm2

### Ans :- 252 cm^{2}.

Explanation :-

Step 1:- Given lengths of parallel sides is 10 and 30 cm .

Length of non parallel sides is 21 and 13 cm

We get a triangle and parallelogram ABED

we get BE = 21 cm ; DE = 10 cm (opposites sides of parallelogram )

CE = CD-DE = 30 - 10 = 20 cm .

Step 2:- Equate the areas and find value of height h

Step 3:-Find the area of trapezium

Therefore, Area of trapezium ABCD = 252 cm^{2}.

### Related Questions to study

### A Hollow cylindrical pipe is 21 cm long. If its outer and inner diameters are 10 cm and 6 cm respectively, then find the volume of the metal used in making the pipe?

### A Hollow cylindrical pipe is 21 cm long. If its outer and inner diameters are 10 cm and 6 cm respectively, then find the volume of the metal used in making the pipe?

### There are 8 people in the lift. Few are ladies and the rest are children. Each lady weighs 150 pounds. Each child weighs 50 pounds. The total weight of the 8 people is 800 pounds. Construct the system of linear equations and use elimination method to solve.

### There are 8 people in the lift. Few are ladies and the rest are children. Each lady weighs 150 pounds. Each child weighs 50 pounds. The total weight of the 8 people is 800 pounds. Construct the system of linear equations and use elimination method to solve.

### If the radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cubic.cm, then find the radius?

### If the radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cubic.cm, then find the radius?

Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

We could also calculate the standard deviation for both the data sets

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.

Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

We could also calculate the standard deviation for both the data sets

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.

### 50 animals are there in a shed. Some of the animals have 2 legs and the rest of them have 4 legs. In total there are 172 legs. Frame the system of linear equations and use elimination method to solve .

### 50 animals are there in a shed. Some of the animals have 2 legs and the rest of them have 4 legs. In total there are 172 legs. Frame the system of linear equations and use elimination method to solve .

### The area of trapezium is 384 sq.cm. If its parallel sides are in the ratio 3:5 and the perpendicular distance between them 12cm. The smaller of the parallel side is

### The area of trapezium is 384 sq.cm. If its parallel sides are in the ratio 3:5 and the perpendicular distance between them 12cm. The smaller of the parallel side is

### A Rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. What is the volume of the cylinder so formed?

### A Rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. What is the volume of the cylinder so formed?

### The difference between two parallel sides of a trapezium is 8cm. The perpendicular distance between them is 19cm while the area of trapezium is 760 sq.cm. What will be the lengths of the parallel sides.

### The difference between two parallel sides of a trapezium is 8cm. The perpendicular distance between them is 19cm while the area of trapezium is 760 sq.cm. What will be the lengths of the parallel sides.

### A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

### A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

### The sum of 3 consecutive natural numbers is 75. Find the numbers.

### The sum of 3 consecutive natural numbers is 75. Find the numbers.

### Find three consecutive even numbers whose sum is 312.

### Find three consecutive even numbers whose sum is 312.

### The base of a parallelogram is thrice of its height .If the area of the parallelogram is 2187 sq.cm , find its height .

Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?

**Note:**

There are three ways to prove that two triangles are similar- AAA,

SAS, SSS.

AAA means that the corresponding angles are equal,

SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,

SSS means that all three corresponding sides have equal ratio

Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?

**Note:**

There are three ways to prove that two triangles are similar- AAA,

SAS, SSS.

AAA means that the corresponding angles are equal,

SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,

SSS means that all three corresponding sides have equal ratio