in figure LM = 18 ft, KM=16 ft and KN=14ft what is the area of KLM
To find the area of triangle KLM, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c can be calculated using the formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, we have LM = 18 ft, KM = 16 ft, and KN = 14 ft.
First, calculate the semiperimeter (s):
s = (18 + 16 + 14) / 2
= 48 / 2
= 24 ft
Next, substitute the side lengths and the semiperimeter into the area formula:
Area = √(24(24-18)(24-16)(24-14))
= √(24(6)(8)(10))
= √(24 * 48 * 10)
= √11520
≈ 107.34 ft²
Therefore, the area of triangle KLM is approximately 107.34 square feet.
Was that supposed to say KL = 14 ?
I will assume that, since N does not enter the picture elsewhere.
Let's find angle K, the largest angle.
18^2 = 14^2 + 16^2 - 2(14)(16)cosK
448cosK = 128
cosK = 2/7
K = appr 73.4°
area = (1/2)(14)(16)sinK
= 112(.9583..)
= appr 107.33 ft^2
for "exact value" :
If cosK = 2/7, then sinK = √(1 - 4/49)
= √45/7
area = (1/2)(14)(16)(√45/7)
= 16√45
which is appr 107.33.. , just like above