Chapter 12: Heron’s Formula

Choose the correct answers:

Q1. The base of a right triangle is 8 cm and hypotenuse is 10 cm . Its area will be :

(A) 24 cm2  (B) 40 cm2         (C) 48 cm2           (D) 80 cm2

Ans:   (A) 24 cm2  .

 [  Using Pythagoras theorem,  

Other side =102-82

 =100-64=36=6 cm

Area of triangle =12×base×altitude

=12×8×6 cm²=24 cm² ]      

Q2. An isosceles right triangle has area 8 cm2 . The length of its hypotenuse is :

(A) 32 cm           (B) 16 cm        (C) 48 cm       (D) 24 cm

Ans:  (A) 32 cm  .         

 [Hints:  A/Q ,  12×b×p=8

 ⇒12×b2=8   ( ∵b=p)

⇒b²⇒16⇒b=16=4 cm 

 Using Pythagoras formula ,

h=p2+b2 

=42+42 cm 

=16+16=32 cm  ]

Q3. The perimeter of an equilateral triangle is 60 m . The area is :

(A) 103 m2  (B)  153 m2         (C)  203 m2           (D)  1003m2

Ans: (D)  1003m2

 [ Hints: Let a be a side of the triangle .

So, a+a+a=60

 ⇒3a=60⇒a=20 cm

Area of equilateral triangle=34a2

=34×400=1003 m²  ]

Q4. The sides f a triangle are 56 cm , 60 cm and 52 cm long . Then the area of the triangle is :

(A) 1322 cm2  (B) 1311 cm2         (C) 1344 cm2           (D) 1392 cm2

Ans: (C) 1344 cm2          

 [Hints: Here, a=56 cm ,  b=60 cm ,  c=52 cm

s=a+b+c2=56+60+522=1682=84 cm

s-a=28 cm , s-b=24 cm , 

 s-c=32 cm 

Area of triangle =ss-as-bs-c

=84×28×24×32 cm2 

=22.3.7.22.7.23.3.25 

 =212.32.72

=26.3.7 cm²=1344cm² ]

Q5. The area of an equilateral triangle with side 23 cm is :

(A) 5.196 cm2  (B) 0.866 cm2         (C) 3.496 cm2           (D) 1.732 cm2

Ans: (A) 5.196 cm2 

  [Hints : Here, a=23 cm

Area of equilateral triangle=34a2

=34×23 2m² 

=34×4×3 m² 

=33 m²  (3=1.732)

=3×1.732 m²=5.196 m²  ]