9th Grade > Mathematics
HERON S FORMULA MCQs
:
A, B, C, and D
Using formula 12×base×height we can find the area of any triangle irrespective of its type if we know the base and the height of the given triangle.
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B
S=Perimeter2 =(2+5+5)2=6 m
Area of the triangle= √s(s−a)(s−b)(s−c)
=√6(6−2)(6−5)(6−5)
=√6×4×1×1
=2√6 m2
Since there are 20 rocks of 4 colours, number of rocks of each colour =204=5
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Therefore the area covered by each type of rock will be =2√6×5 =10√6 m2
:
C
Third side = perimeter - (sum of other two sides) = 38 - 20 = 18 cm
Semi perimeter of a triangle = Perimeter2=382=19 cm
According to heron's formula,
Area of a triangle =√s(s−a)(s−b)(s−c)=√19(19−12)(19−8)(19−18)=√19×7×11×1=√1463 cm2
:
B
Area of a triangle=12×base×height=40
⇒base=40×2height
⇒base=8010=8 cm
:
A
Semi perimeter of a triangle (s) = a+b+c2
⇒8+8+82=12cm
Area of a triangle = √s(s−a)(s−b)(s−c)
=√12(12−8)(12−8)(12−8)
=√12×4×4×4
=√3×4×4×4×4
= 16√3 cm2
:
A
Perimeter = a +b +c (i.e. the sum of length of all the sides)
⇒ Third side = 26 - 8 - 6
= 26 - (8+6)
= 26 - 14
=12
Third side = 12 cm
:
B
Area of triangle = 12×base×height
The hypotenuse is the longest side of a right-angled triangle. Hence, the base and the height are 6 cm and 8 cm.
∴area=12×6×8
=24 cm2
:
Using the Heron's formula, Area (A)= √s(s−a)(s−b)(s−c).
Semi-Perimeter (s) = a+b+c2 =11+15+62
=16 m
∴A=√16(16−11)(16−15)(16−6) =20√2 m2
3 and a half years = 12 x 3 + 6 = 42 months.
∴ Earning in 3 and a half years =20√2×1000×42 =Rs.840000√2
The value of A is 840000.
:
a=6 cm,b=8 cm,c=10 cm
s=a+b+c2
s=6+8+102
=12cm
A=√s(s−a)(s−b)(s−c)
A=√12(12−6)(12−8)(12−10)
=24 cm2
The cost of painting it =24×25=600 paise
=Rs. 6