Math problem on area?

Question

http://img383.imageshack.us/img383/4365/picture1lh3.png

how do i calculate the area of the shape?

Answer 1

(5 x 4)/2 + 8(9 + 8 + 7) + 3 x 8 + 3(12 - 8)/2

= 20/2 + 8(24) + 24 + 3(4)/2

= 10 + 192 + 24 + 12/2

= 202 + 24 + 6

= 226 + 6

= 232 square units

Answer 2

Name the shape as ABCDEFGHIJK from the upper right corner.

Now, name the intersection of line AB and JK as L.

BL = GH

AL = AB-BL = AB-GH = 12-8 = 4

By Phytagorean Theorm on triangle AKL: KL = 3

HJ + JK + KL = BC + DE + FG

HJ + 17 + 3 = 7 + 8 + 9

HJ = 4

Area total = Area HIJ + Area KAL + Area HLBF + Area CDEF

=5x4/2 + 4x3/2 + 8x24 + 8x3 = 232

Answer 3

232

Answer 4

Divide it into rectangles and triangles. You know how to work out the area of those don't you?

Answer 5

SAM E-T did a good job up there:

The bottom rectangle is  (3 * 8 = 24)

The middle rectangle is  (24 * 8 = 192)

The top right triangle is  (1/2 * 3 * 4 = 6)

The top left triangle  (1/2 * 4 * 5 = 10)

24+192+6+10=232

Answer 6

We need to break this up into parts.

There are 4 parts of this shape, the middle rectangle, the right triangle, the left triangle, and the bottom rectangle.

We can start with the bottom rectangle.

We know that its dimensions are 3x8, so its area is 24. (3 * 8 = 24)

Next is the middle rectangle.

We know that one side is 9 + 8 + 7, and the other is 8, so its area is 192. (24 * 8 = 192)

Next is the top right triangle.

We know that its height is 12-8, and we can find its width using Pythagoras' theorem. c^2 - a^2 = b^2. Since we know that the hypotenuse(c) is equal to 5, and the height is equal to 4, we can establish that the width is equal to the square root of 25-16, or 3. From this we can establish that the area of the triangle is 6. (1/2 * 3 * 4 = 6)

Finally, the top left triangle.

We know that its height is 5, and that its width is (9+8+7)-(17+3), or 4. So we can establish that its area is 10. (1/2 * 4 * 5 = 10)

Then, we add them all together to get the final area of the shape, 232.

This should be correct, I know I just answered a question and then after I posted it found out that I used the wrong value for one of the variables.