(Note: Figure is not drawn to scale.)

4. The area of the above figure ABCD

A) is 36
B) is 108
C) is 156
D) is 1872
E) Cannot be determined
Answer:

(A) You are right! Use Strategy 14, p. 104; BASIC SKILLS - Mini Math Refresher - Areas, p. 161; Right Triangles, p. 162; Math Refresher (306), p. 222, and (509), p. 276: The best way to do the problem is to draw or extend lines to get more information. Draw BD, then find length BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 x 4/2 = 6 and the area of triangle BDA to be 5 x 12 /2 = 30. So the sum of these areas is the area of the figure ABCD. 36 is the answer.

(B) No. Use Strategy 14, p. 104; BASIC SKILLS - Mini Math Refresher - Areas, p. 161; Right Triangles, p. 162; Math Refresher (306), p. 222, and (509), p. 276: The best way to do the problem is to draw or extend lines to get more information. Draw BD, then find length BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 x 4/2 = 6 and the area of triangle BDA to be 5 x 12 /2 = 30. So the sum of these areas is the area of the figure ABCD. 36 is the answer.

(C) No. Use Strategy 14, p. 104; BASIC SKILLS - Mini Math Refresher - Areas, p. 161; Right Triangles, p. 162; Math Refresher (306), p. 222, and (509), p. 276: The best way to do the problem is to draw or extend lines to get more information. Draw BD, then find length BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 x 4/2 = 6 and the area of triangle BDA to be 5 x 12 /2 = 30. So the sum of these areas is the area of the figure ABCD. 36 is the answer.

D) Did you multiply the sides to get 1872? Now come on, you would'nt bet $100 on that would you?
Use Strategy 14, p. 104; BASIC SKILLS - Mini Math Refresher - Areas, p. 161; Right Triangles, p. 162; Math Refresher (306), p. 222, and (509), p. 276: The best way to do the problem is to draw or extend lines to get more information. Draw BD, then find length BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 x 4/2 = 6 and the area of triangle BDA to be 5 x 12 /2 = 30. So the sum of these areas is the area of the figure ABCD. 36 is the answer.

(E) No. Notice that the length of BD is determined. This means the area of triangles BCD and BDA are determined. So the sum of the areas of the two triangles are determined, and so the area of figure ABCD is determined.

Use Strategy 14, p. 104; BASIC SKILLS - Mini Math Refresher - Areas, p. 161; Right Triangles, p. 162; Math Refresher (306), p. 222, and (509), p. 276: The best way to do the problem is to draw or extend lines to get more information. Draw BD, then find length BD. BD = 5 because triangle BCD is a 3-4-5 right triangle. Now triangle BDA is also a right triangle because a 5-12-13 triangle is a right triangle. We can then find the area of triangle BCD to be 3 x 4/2 = 6 and the area of triangle BDA to be 5 x 12 /2 = 30. So the sum of these areas is the area of the figure ABCD. 36 is the answer.