What is the area of this property in m?
The area of this property is 7800 m^2.
A = b x h
A = 130 x 120 = 15600 m^2
A = 1/2bh
A = 1/2(130)(120) = 7,800 m^2 answer//
Let the length of one leg be L .
The length of this isosceles triangle is 130 , so
the height of this triangle is
√(L^2 - (130/2)^2) = √(L^2 - 4225)
So the area S of this triangle is
S = (1/2)130√(L^2 - 4225) = 65√(L^2 - 4225)
On the other hand , the altitude from one of the legs is 120 , so
the area S of this triangle is
S = (1/2)120L = 60L
Therefore
65√(L^2 - 4225) = 60L
4225(L^2 - 4225) = 3600L^2
625L^2 = 4225^2
L^2 = 28561
L = 169
So S becomes
S = 60*169 = 10140 [m^2]
(Of course , S = 65√(169^2 - 4225) = 65√24336 = 10140)
The altitude is from one of the legs, right? Let each leg have a length of x + y
120^2 + x^2 = 130^2
x^2 = 16900 - 14400
x^2 = 2500
x = 50
y^2 + 120^2 = (x + y)^2
y^2 + 14400 = (50 + y)^2
y^2 + 14400 = 2500 + 100y + y^2
14400 = 2500 + 100y
144 = 25 + y
119 = y
x + y = 50 + 119 = 169
The base is 130, so half the base is 65
65^2 + h^2 = 169^2
25 * 13^2 + h^2 = 13^2 * 13^2
h^2 = (169 - 25) * 13^2
h^2 = 144 * 13^2
h = 12 * 13
h = 156
(1/2) * 156 * 130 =>
78 * 130 =>
13 * 13 * 6 * 10 =>
169 * 6 * 10 =>
338 * 3 * 10 =>
(990 + 24) * 10 =>
1014 * 10 =>
10140
10140 square meters
Using Heron's formula
s = (169 + 169 + 130) / 2 = 169 + 65 = 234
sqrt(s * (s - 169) * (s - 169) * (s - 130)) =>
(s - 169) * sqrt(s * (s - 130)) =>
(234 - 169) * sqrt(234 * (234 - 130)) =>
65 * sqrt(234 * 104) =>
65 * sqrt(9 * 26 * 26 * 4) =>
65 * 3 * 26 * 2 =>
130 * 78 =>
130 * (80 - 2) =>
10400 - 260 =>
First use formula in pic to find 'h' since you know b & s(altitude)
h = √(s² -(b/2)²)
A = 1/2bh = 1/2 b*√(s² -(b/2)²)
insert your numbers
I get 6557m²
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Answers & Comments
The area of this property is 7800 m^2.
A = b x h
A = 130 x 120 = 15600 m^2
A = 1/2bh
A = 1/2(130)(120) = 7,800 m^2 answer//
Let the length of one leg be L .
The length of this isosceles triangle is 130 , so
the height of this triangle is
√(L^2 - (130/2)^2) = √(L^2 - 4225)
So the area S of this triangle is
S = (1/2)130√(L^2 - 4225) = 65√(L^2 - 4225)
On the other hand , the altitude from one of the legs is 120 , so
the area S of this triangle is
S = (1/2)120L = 60L
Therefore
65√(L^2 - 4225) = 60L
4225(L^2 - 4225) = 3600L^2
625L^2 = 4225^2
L^2 = 28561
L = 169
So S becomes
S = 60*169 = 10140 [m^2]
(Of course , S = 65√(169^2 - 4225) = 65√24336 = 10140)
The altitude is from one of the legs, right? Let each leg have a length of x + y
120^2 + x^2 = 130^2
x^2 = 16900 - 14400
x^2 = 2500
x = 50
y^2 + 120^2 = (x + y)^2
y^2 + 14400 = (50 + y)^2
y^2 + 14400 = 2500 + 100y + y^2
14400 = 2500 + 100y
144 = 25 + y
119 = y
x + y = 50 + 119 = 169
The base is 130, so half the base is 65
65^2 + h^2 = 169^2
25 * 13^2 + h^2 = 13^2 * 13^2
h^2 = (169 - 25) * 13^2
h^2 = 144 * 13^2
h = 12 * 13
h = 156
(1/2) * 156 * 130 =>
78 * 130 =>
13 * 13 * 6 * 10 =>
169 * 6 * 10 =>
338 * 3 * 10 =>
(990 + 24) * 10 =>
1014 * 10 =>
10140
10140 square meters
Using Heron's formula
s = (169 + 169 + 130) / 2 = 169 + 65 = 234
sqrt(s * (s - 169) * (s - 169) * (s - 130)) =>
(s - 169) * sqrt(s * (s - 130)) =>
(234 - 169) * sqrt(234 * (234 - 130)) =>
65 * sqrt(234 * 104) =>
65 * sqrt(9 * 26 * 26 * 4) =>
65 * 3 * 26 * 2 =>
130 * 78 =>
130 * (80 - 2) =>
10400 - 260 =>
10140
First use formula in pic to find 'h' since you know b & s(altitude)
h = √(s² -(b/2)²)
A = 1/2bh = 1/2 b*√(s² -(b/2)²)
insert your numbers
I get 6557m²