We can divide the H into four rectangles and two triangles, as shown in the image below:
[asy]
pair A,B,C,D,E,F,P,Q,R,S;
A = (0,0);
B = (12,0);
C = (12,3);
D = (5,3);
E = (5,9);
F = (0,9);
P = (0,3);
Q = (12,9);
R = (12,6);
S = (5,6);
draw(A--B--C--D--E--F--cycle);
draw(P--Q);
draw(R--S);
label("$3$", (B+C)/2, N);
label("$12$", (A+B)/2, S);
label("$5$", (D+E)/2, E);
label("$5$", (P+F)/2, W);
label("$6$", (R+C)/2, W);
[/asy]
The areas of the rectangles are:
- 3x12 = 36 (top rectangle)
- 6x12 = 72 (bottom rectangle)
- 3x5 = 15 (right rectangle)
- 6x5 = 30 (left rectangle)
The areas of the triangles are:
- (1/2)(5)(3) = 7.5 (top triangle)
- (1/2)(6)(5) = 15 (bottom triangle)
Therefore, the total area is:
36 + 72 + 15 + 30 + 7.5 + 15 = 175.5
Rounding to the nearest whole number, we get 176, which is not one of the answer choices. However, we can see that option C (77 square units) is much too small, so the closest answer choice is option A (83 square units). Therefore, the answer is A.
Use the image to answer the question.
An illustration shows the outline of letter upper H. The two vertical sides of the outline letter upper H have length 12 and width 3. The horizontal part across the middle has length 5. The inner side of the upper vertical part of the H has length 5. The inner side of the lower vertical part has length 6.
What is the area of the polygon?
A. 83 square units
B. 72 square units
C. 77 square units
D. 68 square units
1 answer