Question

The area of trapezoid TRAP is 100. Furthermore, TR = 32, AP = 8, and TP = RA. If AngleT = AngleR, what is the length of segment TP?

Answer 1

TP: 13

Explanation:

A=((b1+b2)/2)*h

100=((8+32)/2)*h

100=(40/2)*h

100=20h

h=5

A=8*5+((32-8)/2)*0.5*5*2

100=40+(24/2)*5

60=12*5

thus, point E is is 12 away from T

Triangle TPE:

the catets are TE:12 and PE:5

Lets use the Pythagorean theorem:

a^2+b^2=c^2

12^2+5^2=c^2

144+25=c^2

169=c^2

c=(+/-)13

since distance can only be positive, the answer is:

segment TP has the length of 13 units