Area, General Mathematics

Question: If x is the length of a median of an equilateral triangle, then its area is :
A
`x^2`

B
`1/2 x^2`

C
`(x^2sqrt(3))/2`

D
`(x^2sqrt(3))/3`

Note: `(Area of square)/(Area of triangle)` `= a^2/sqrt(3)/4 a^2` `= 4/sqrt(3), i. e. 4: sqrt(3)`
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Question: If x is the length of a median of an equilateral triangle, then its area is :
A
`x^2`

B
`1/2 x^2`

C
`(x^2sqrt(3))/2`

D
`(x^2sqrt(3))/3`

Note: `(Area of square)/(Area of triangle)` `=( a^2)/(sqrt(3))/(4) a^2` `= 4/sqrt(3), i. e. 4: sqrt(3)`
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Question: If x is the length of a median of an equilateral triangle, then its area is :
A
`x^2`

B
`1/2 x^2`

C
`(x^2sqrt(3))/2`

D
`(x^2sqrt(3))/3`

Note: `(Area of square)/(Area of triangle)` `= a^2/sqrt(3)/4 a^2` `= 4/sqrt(3), i. e. 4: sqrt(3)`
1. Report
Question: If x is the length of a median of an equilateral triangle, then its area is :
A
`x^2`

B
`1/2 x^2`

C
`(x^2sqrt(3))/2`

D
`(x^2sqrt(3))/3`

Note: Let the side of the triangle be a. `a^2 = (a/2)^2 + x^2 or (3a^2)/4` `x^2 or a^2 = (4x^2)/3.` :. Area` = sqrt(3)/4 a^2` ` = sqrt(3)/4 xx 4/3 x^2` `= x^2/sqrt(3)` `= (x^2sqrt(3))/3`
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Question: The altitude of an equilateral triangle of side` 3sqrt(3)` cm is :
A
3 cm

B
`2sqrt(3) cm`

C
`4.5 cm`

D
`sqrt(3)/4 cm`

Note: Area` = sqrt(3)/4 xx (3sqrt(3)^2)` `= (27sqrt(3))/4.` Now` 1/2 xx 3sqrt(3) xx height` `= (27sqrt(3))/4` :. Height` = (27sqrt(3))/4 xx 2/(3sqrt(3))` `= 9/2 = 4.5 cm.`
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Question: A triangle of area `(9 xx y) cm^2` has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. Then, the value of y is :
A
`sqrt(2)`

B
`sqrt(3)`

C
`2`

D
`3`

Note: `sqrt(3)/4 xx (6 xx 6)` `= 9 xx y => y = sqrt(3)`
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Question: If the area of a square with side a is equal to the area of a triangle with base a then, the altitude of the triangle is :
A
`a/2`

B
`a`

C
`2a`

D
`4a`

Note: `1/2 xx a xx `altitude` = a^2 => altitude = 2a.`
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Question: The area of a right angled triangle is 30 sq.cm and the length of its hypotenuse is 13 cm. The length of the shorter leg is :
A
4 cm

B
5 cm

C
6 cm

D
7 cm

Note: Let the order sides be x and y Then, `x^2 + y^2 = (13)^2` `= 169.` Also, `1/2 xy = 30 => xy = 60` `:. (x + y) = sqrt(x^2 + y^2) + 2xy` `= sqrt(169 + 120)` `= sqrt(289)` `= 17` `(x - y) = sqrt((x^2 + y^2)) - 2xy` `= sqrt(169 - 120)` `= sqrt(49)` `= 7` Solving x + y = 17, x - y = 17, x - y = 7, we get x = 12 x = 12 and y = 5
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Question: In a ABC we have : BC = 5 cm, AC = cm and AB = 13 cm. The length of the altitude drawn from B on AC is :
A
4 cm

B
5 cm

C
6 cm

D
7 cm

Note: a = 5, b = 12 and c = 13 `:. s = 1/2 (5 + 12 + 13) cm = 15 cm.` :. Area` = sqrt(15 xx 10 xx 3 xx 2)` `= 30 cm^2` `1/2 xx 12 xx Height = 30 => Height = 5 cm.`
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Question: If the circumference of a circle is 352 metres, then its area (in sq.m) is :
A
5986

B
6589

C
8956

D
9856

Note: `2
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Question: If x is the length of a median of an equilateral triangle, then its area is :

Question: If x is the length of a median of an equilateral triangle, then its area is :

Question: If x is the length of a median of an equilateral triangle, then its area is :

Question: If x is the length of a median of an equilateral triangle, then its area is :

Question: The altitude of an equilateral triangle of side` 3sqrt(3)` cm is :

Question: A triangle of area `(9 xx y) cm^2` has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. Then, the value of y is :

Question: If the area of a square with side a is equal to the area of a triangle with base a then, the altitude of the triangle is :

Question: The area of a right angled triangle is 30 sq.cm and the length of its hypotenuse is 13 cm. The length of the shorter leg is :

Question: In a ABC we have : BC = 5 cm, AC = cm and AB = 13 cm. The length of the altitude drawn from B on AC is :

Question: If the circumference of a circle is 352 metres, then its area (in sq.m) is :