## Area of Right triangle:-

### Today in this article I want to discuss with you the topic area of right triangle,to start my discussion let us know,

## **What is a right triangle?

### Answer:- A triangle whose any one angle measures 90° is called right triangle.

### In the picture,

ABC is a right triangle,whose <B=90°

### Now we will learn

## ***what is the area of right triangle?

### Answer:- The area of right triangle

### can be defined the total inside space covered by the three sides of the triangle.

Again,

we can explain

The area of right triangle = ½ × base×perpendicular/height

## Problems related on area of right triangle:-

## Question(1):- The base of a right triangle is 4cm and its height is 6cm, find its area.

### Answer:-

### ∵ Base of right triangle(b)= 4cm

and height/perpendicular of right triangle(p) = 6cm

∴ area of right triangle = ½ ×b ×p

= ½ ×4×6

= (2×6)m²

= 12m²

## **Question(2):- The area of a right triangle is 15 cm² and its perpendicular is 3 cm, find its base.

### Answer:-

### 1st method,

### ∵The area of right triangle(A)=15cm²

perpendicular(p) = 3 cm

∴ base of the triangle(b)= 2×A/p

= (2×15)/3

= 30/3

= 10cm

### 2nd method,

### ∵The area of right triangle(A)=15cm²

### perpendicular(p) = 3 cm

Let the base of the right triangle =b cm

Now, According to question,

½ × b × p = 15

=>½ × b × 3 =15

=> b × 3 = 15 × 2

=> b × 3 = 30

=> b = 30/3

=> b =10

∴ Base of the right triangle(b) = 10 cm

## Question(3):- The area of a right triangle is

20 cm² and its base 5 cm find its height/perpendicular.

### Answer:-

### 1st method:-

### ∵ Area of right triangle(A) = 20cm²

Base of right triangle(b) = 5 cm

∴ height/perpendicular(h/p)= 2×A/b

= 2× 20/5

= 40/5

= 8 cm

### 2nd method:-

### ∵ Area of right triangle(A) = 20cm²

### Base of right triangle(b) = 5 cm

Let, perpendicular = p cm

Now,according to question,

½ × b × p = 20

=>½ ×5×p = 20

=>5×p = 2×20

=>5×p = 40

=> p = 40/5

=>p = 8

∴ perpendicular = 8 cm

When we say right triangle there must be mention the famous law of Pythagorus.

### So, I am explaining 'Pythagorus law':-

### "Pythagorus law states that sum of the squares of base and perpendicular of a right triangle is equal to the square of its hypotenuse"

## Application of Pythagorus law:-

## Question(1):-Perpendicular drawn from the vertex A of Δ ABC intersect BC at D, such that DB=3CD, Prove that 2AB²= 2AC² +BC²

### Answer:-

### In the picture, AD⊥BC in Δ ABC is drawn,which intersects BC at point D,such that DB=3CD ∴ BC=DB+CD

=>BC =3CD+CD

=>BC = 4CD

### To prove:- 2AB²=2AC²+BC²

### Proof:- In right triangle ADB,

### Applying Pythagorus law, we find

∵ AB²= AD²+ BD² [∵<ADB = 90°]

=>2AB²=2AD²+2BD²—---------(1)[∵multiplying both sides by 2]

Again,in right triangle ADC,

Applying Pythagorus law, we find

∵ AC² = AD² + CD² [∵ <ADC =90°]

=>2AC²=2AD²+2CD²—----(2)[∵multiplying both sides by 2]

###

Now equation(1) -equation(2) we get,

2AB²-2AC² = 2BD²- 2CD²

=>2AB² - 2AC² = 2(3CD)² - 2CD² [∵ putting DB =3CD]

=>2AB² - 2AC² = 18CD² - 2CD²

=>2AB² - 2AC² = 16CD²

=>2AB² - 2AC² = (4CD)²

=>2AB² - 2AC² = (BC)² [∵putting 4CD= BC]

=>2AB² - 2AC² = BC²

### =>2AB² = 2AC² +BC²

### Proved

## More Question:-

# Question(2):- In Δ ABC, <C=90°, D and E are two points on the sides CA and CB,Prove that, AE² + BD² = AB² + DE²

### Answer:-

### In the picture, ABC is a Δ, whose <C =90° Dand E are two points on the sides CA and CB,

### To prove:-AE² + BD² = AB² + DE²

### Proof:- ∵ In right triangle ABC,

### we get,

∵ AB² = AC² + BC²—-----(i)

=> AE² = AC² + CE²—---(ii)

=>BD² = BC² +CD²—----(iii)

=>DE² = CE² + CD²—---(iv)

## FREQUENTLY ASKED QUESTIONS:-
## What is the four walls formula of a cube?

Answer: The four walls area formula of a cube = 4l² where, l = length of each face of the cube.

## what is the total surface area formula of a cube ?

Answer:- The total surface area formula of a cube = 6ll² where, l= length of each face of the cube.

## what is the ceiling area formula of a house?

Answer :- The ceiling area formula of a house = l × b where, l = length of the house and b = breadth of the house.

## What is four walls area formula of a cuboid ?

Answer :- The four walls formula of a cuboid = 2(l+b)h where, l = length of the cuboid, b = breadth of the cuboid and h = height of the cuboid.

##
What is curved surface area formula of a cylinder?

Answer:-The curved surface area formula of a cylinder = 2πrh where, r = radius of the cylinder and h = height of the cylinder.

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

Answer :- Curved surface area formula of a cone = πrl where, r = radius of the cube,
and l = slent height of the cone.

## What is the four walls formula of a cube?

Answer: The four walls area formula of a cube = 4l² where, l = length of each face of the cube.

## what is the total surface area formula of a cube ?

Answer:- The total surface area formula of a cube = 6ll² where, l= length of each face of the cube.

## what is the ceiling area formula of a house?

Answer :- The ceiling area formula of a house = l × b where, l = length of the house and b = breadth of the house.

## What is four walls area formula of a cuboid ?

Answer :- The four walls formula of a cuboid = 2(l+b)h where, l = length of the cuboid, b = breadth of the cuboid and h = height of the cuboid.

## What is curved surface area formula of a cylinder?

Answer:-The curved surface area formula of a cylinder = 2πrh where, r = radius of the cylinder and h = height of the cylinder.

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

Answer :- Curved surface area formula of a cone = πrl where, r = radius of the cube, and l = slent height of the cone.