Problem:
The area of the triangle bounded by the lines y=x,y=−x and y=6 is
Answer Choices:
A. 12
B. 122​
C. 24
D. 242​
E. 36
Solution:
Let O be the origin, and let A and B denote the points where y=6 intersects y=x and y=−x respectively. Let OL denote the altitude to side AB of △OAB. Then OL=6. Also, AL=BL=6. Thus, the area of △OAB is
21​(AB)(OL)=21​⋅12⋅6=36.
OR
Let A′=(6,0). Then △A′OA≅△LOB, so the area of triangle AOB equals the area of square A′OLA, which is 62=36.
OR
Use the determinant formula for the area of the triangle: 21​∣∣∣∣∣∣∣​06−6​066​111​∣∣∣∣∣∣∣​=36.
