Sonia G.
asked • 02/20/17Trigonometry- Area of Quadrilateral
Find area of quadrilateral ABCD with AB= 12cm, BC=10 cm, and CD=10 cm, angle B = 108 degres, and angle C = 132 degrees.
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2 Answers By Expert Tutors
Doug C. answered • 02/21/17
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Math Tutor with Reputation to make difficult concepts understandable
Here is an alternative for solving this problem. After drawing segment BD, triangle BCD is isosceles with legs 10 and vertex angle (C) 132. You can find the base angles of that triangle, which will allow you to determine the measure of <ABD. You can use straightforward trig ratios to find the length of BD after dropping the altitude from C to BD. Then you have enough info to calculate the area of triangle ABD too.
Mark M. answered • 02/20/17
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Mathematics Teacher - NCLB Highly Qualified
Draw and label a diagram.
Draw the diagonal DB and label it d.
AreaDCB = 0.5(10)(10)sin 132°
Use Law of Cosines to determine "d."
Use Law of Sines to determine ∠DBC.
Calculate ∠ABD
Use that angle, 12, and d to determine are of triangle
Add are of triangles.
Sonia G.
Is this quadrilateral a trapezoid?
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02/20/17
Mark M.
I do not have enough information to determine.
What values did you determine?
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02/20/17
Sonia G.
I only have 132 degrees and 108 degrees. When drawing and labeling a diagram, I get a trapezoid.
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02/20/17
Sonia G.
How do you calculate angle ABD?
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02/20/17
Mark M.
Which two sides are parallel?
m∠ABD = 108° - m∠DBC
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02/20/17
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Sonia G.
02/20/17