Question

After receiving a grant for music education, a school decides to build a new band room for its expanded music program. Quadrilateral ABCD represents the floor plan of the new band room. What is the area of the room?
AE = 32 ft.
BE = 12 ft.
CE = 26 ft.
DE = 26 ft.
There is a diagram. The scale is off.

B
/|\
/ | \
/ | \
/ | \
/ | \
/ |-| \
A------E------C
\ | /
\ | /
\ | /
\ | /
\ | /
\D/
I need the formula please.
Possible answers
1102ft sq
2288ft sq
1008ft sq
2204ft sq

Thank you.

Answer 1

E is the point of intersection of AC and BD.so AC=58 ft which is AE+CE=32+26= 58.
Now we have 2 triangles ACB and ACD.
Area of triangle ACB= base.height/2
58 times12/2=348 ftsquare
Area of triangle ACD=58 times 26/2=754 square ft
To find the area of the quadrilateral ,we add the areas of two triangles which is 348+ 754= 1102 ft square