Geometry

1) In the diagram below, if $AD=30$, what is $BC$?

[asy] size(5cm); pair A,B,C,D; B=(0,0); A=(0,8); C=(12,0); D=(12,-2); draw(A–B–C–D–A); draw(rightanglemark(C,B,A,20)); draw(rightanglemark(D,C,B,20)); label(“$A$”,A,NW); label(“$B$”,B,SW); label(“$C$”,C,NE); label(“$D$”,D,SE); label(“$11$”,A–B,W); label(“$4$”,C–D,E); [/asy]

2) If $ST = 2,$ $QS = 4,$ and $PT = 5,$ find $PQ.$
image: https://latex.artofproblemsolving.com/a/7/e/a7eab5e61bab7da8c73b574bd4b0aef92559ee50.png

3) Find the Area of the Triangle

Image: https://latex.artofproblemsolving.com/5/9/d/59d222805a6bec04663b50d269dbc9bf8562488b.png

——————————————————————————————————————————————————-

1) Given that $AB+CD = 20,$ what is $BD?$

Image: https://latex.artofproblemsolving.com/c/e/a/cea4f110ff0546a5f823da68bc7f20a2cb27d19b.png

2) Find QS

Image: https://latex.artofproblemsolving.com/1/1/d/11dc66b67019b54254f79d4b2604d2c5f497ff19.png

3) Find the Area of the rectangle

Image: https://latex.artofproblemsolving.com/e/a/9/ea93148bb0fba5a0441b2354fd0f981da4d4a6d6.png

4) ll five rectangles in the diagram are congruent. If the short side of each rectangle is 1 then find the long side of each rectangle

Image: https://latex.artofproblemsolving.com/4/7/3/473a88995b68257533aac77f37cd60576f455785.png

5)Find AC

Image: https://latex.artofproblemsolving.com/9/f/6/9f68656be38cdc0b51645684ad79072e1e3ef802.png