Calculate the area of the shape below.
2 answers:
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Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L =
cos ∠L =
∠L = cos⁻¹
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
Answer:
The Area of Δ ABC = 219.13
Step-by-step explanation:
<em>The hard part about this problem is finding the area without the height</em>
The formula to do this is Area =
A, B, C represent the sides
S represents (A + B + C)
In this equation, we will make the base be A, and the other two sides will be B and C
<u>Sides B and C are the same length</u> because they meet at a 90° angle
Lets plug the numbers into the variables
A = 28
B= 21
C= 21
<u>Remember:</u> S represents (A + B + C)
S = (28 + 21 + 21)
S = (70)
S = 35
<em>Lets plug the numbers into the Area Formula now!</em>
Area =
According to the order of operations, we need to do the calculations in parentheses <u>first</u>
35 - 28 = 7
35 - 21 = 14
35 - 21 = 14
14 x 14 x 7 = 1372
1372 x 35 = 48020
= 219.13
The Area of Δ ABC = 219.13