The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².
<h3>What is the Area of a Rectangle?</h3>
Area of a rectangle = (length)(width).
<h3>Given the following:</h3>
Angle of measure 78 degree enclosed by the diagonals of the rectangle
Perimeter = 36 cm
To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.
A side of the rectangle = x cm
The other side = (36 - 2x)/2 = (18 - x) cm
Angle of the diagonal base = (180 - 78)/2 = 51°
Apply the tangent ratio to find x:
Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,
∅ = 51°
Opposite side = x cm
Adjacent side = (18 - x) cm
Tan 51° = x/(18 - x)
1.235 = x/(18 - x)
1.235(18 - x) = x
22.23 - 1.235x = x
22.23 = x + 1.235x
22.23 = 2.235x
22.23/2.235 = 2.235x/2.235
x = 9.946 cm (one side length)
The other side length = 18 - x = 18 - 9.946 = 8.054 cm
Area of the rectangle = (9.946)(8.054)
Area of the rectangle = 80.1 cm²
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