geometry
posted by Anonymous .
ABCD is a trapezoid with AB parallel to DC. If AB=25, BC=24, CD=50 and AD=7, what is the area of ABCD?

We are going to need some sort of angle.
draw BE  AD, then ABED is a parallelogram and BE = 7
In triangle BCE,
BC = 24
BE = 7
CE = 5025 = 25
by the cosine law:
7^2 = 24^2 + 25^2  2(24)(25)cosC
cosC = 1152/1200
angle C = 16.26...  I stored the entire number
we can now find the height:
sin 16.26... = height/24
height = 24sin16.26.. = 6.72  that came out exact
area = (1/2)(25+50)(6.72) = 252 square units
Respond to this Question
Similar Questions

Geometry
Figure ABCD is a trapezoid with DC = (1/3) AB. What is the ratio of area ABCD to area DCE? 
math
Trapezoid ABCD, top and bottom are parallel. Left is 45, bottom is 60, right is 30, top is unknown. Trapezoid EFGH is similar to ABCD, top and bottom are parallel. Top is 10, other sides are unknown. Area of ABCD is 9 times larger … 
grade 9 math
Trapezoid ABCD, top AD and bottom BC are parallel. AD is the smaller of the two parallel lines. Left AB is 45, bottom BC is 60, right CD is 30, top AD is unknown. Trapezoid EFGH is similar to ABCD, top EH and bottom FG are parallel. … 
Math
Given a trapezoid ABCD with AD parallel to BC. The diagonals AC and BD are congruent. Prove that ABCD is an isosceles trapezoid. 
Math
Given a trapezoid ABCD with AD parallel to BC. The diagonals AC and BD are congruent. Prove that ABCD is an isosceles trapezoid. 
maths
ABCD is a trapezoid with AB parallel to DC. If AB = 25, BC = 24, CD = 50 and AD = 7, what is the area of ABCD? 
GEOmetry!!.....
ABCD is a trapezoid with AB<CD and AB parallel to CD. Γ is a circle inscribed in ABCD, such that Γ is tangent to all four sides. If AD=BC=25 and the area of ABCD is 600, what is the radius of Γ? 
Geometry
ABCD is a trapezoid with AB < CD and AB parallel to CD. \Gamma is a circle inscribed in ABCD, such that \Gamma is tangent to all four sides. If AD = BC = 25 and the area of ABCD is 600, what is the radius of \Gamma? 
Geometry
I have four questions: 1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid. 2. In trapezoid ABCD, line BC is parallel … 
Geometry
Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?