i dont get the steps to this problem?

Question

http://i66.photobucket.com/albums/h267/irvingtons_girl_power/math3.jpg

how do i find the area of the shaded part?

it doesn't have any sq signs or anything! just a stupid diamond in a box!

Answer 1

do your own

Answer 2

The easiest way to do this would be to figure the area of the rectangle and then subtract off the areas of the triangles.

The length of the rectangle is (6+8) = 14
The width of the rectangle is (3+4) = 7
So the area of the rectangle is 7x17 = 98

Now you have to subtract off four triangles. These all appear to be right triangles, let's assume they are. (If they weren't then the outside figure wouldn't be a rectangle, and the figure would have to include angles on it. It doesn't, so we can safely assume that the figure is what it appears to be, a rectangle, and so the four cutouts are right triangles)

Ok, here goes --
The triangles are 4x8, 4x6, 3x8, and 3x6
The combined area of these triangles is
1/2(4x8) + 1/2(4x6) + 1/2(3x8) + 1/2(3x6)
If you like you can factor out the 1/2 or you can simply add these up, either way you get 49

Subtract the combined area of the triangles, 49, from the area of the rectangle, 98, and you get the shaded area, 49

Since there are no units given you'll have to keep it generic and say the shaded area is 49 square units. Which happens to be half the area of the rectangle. Fortunately you don't have to figure out if this is true for in general, but if you did, that would be doable, as a problem in geometry.

That wasn't so bad, was it?

Answer 3

just find the area of the two triangles and add them up...
if u see the shaded region can be divided into two triangles, one on the top, one on the bottom

here's how to do it,
use the formula for finding out the area of a triangle

****

area of the first triangle

(1/2)*base length*height

=(1/2)*14*3

=21 cm squared

area of the second triangle

(using the same formula, from line 4)

(1/2)*14*4

= 28 cm squared

therefore, the area of the total shaded region is


28+21
= 49 cm squared

now i'm saying CM squared, cuz u didnt tell me the units for ur problem, so i'm just taking it as cm, if it's M, then put in M squared ... u get the point right? i hope it helps


p.s. if it doesnt have any units just take cm squared, because that's the standard for problems like these

Answer 4

These problems almost always require you to find the area of the whole thing (the rectangle in this case) and then subtract the white parts, leaving the shaded part.

The rectangle is easy, right? And, each of the white parts is a right triangle whose area is 1/2 * base * height, all of those being given.

If you don't assume this is a rectangle, you do know it is a parallelogram (both pairs of opposite sides congruent). Now you can at least say the area of the diamond is 1/2 the area of the whole parallelogram.

Answer 5

You could get the area of the whole figure then subtract the area of the unshaded part to get the area of the shaded part. The unshaded part consists of 4 triangles. How can you get the area of a triangle? Just simply multiply the 2 given measurements of each side of the given triangle then divide it by 2. After getting the area of the 4 unshaded parts, add them all up then subtract it to the area of the whole part.

Answer 6

1/2 total area = 1/2 * 14 * 7 = 49. to see this break into 4 blocks 3*6, 8*3, 4*6, 8*4. note each block is 1/2 shaded.

Answer 7

first you find the area of the rectangular box.that is
(8+6)*(4+3)
=14*12
=168cm^2
then find the area of the four triangles in the box.you can find the hypotenuse of the four triangles by pythagorus theorem.then add the areas of the four triangles and subtract the total sum of the areas of the four triangles from area of the rectangular box.this area is the area of the shaded portion.

Answer 8

Find the area of the entire figure by multiplying the length by the width.

then find the area of the four white triangles in each corner

then subtract the area of the four triangles from the entire figure and you will have the answer

Answer 9

GIVEN:
The rectangle ABCDEFGHA
AB = 6
BC = 8
CD = 3
DE = 4
EF = 6
FG = 8
GH = 4
HA = 3

CALCULATIONS
Area of ABCDEFGHA = (6 + 8)(3 + 4) = 98
Area of ABH = 1/2 x 6 x 3 = 9
Area of BCD = 1/2 x 8 x 3 = 12
Area of DEF = 12
Area of FGH = 16
AREA OF BDFH = 98 - 9 - 12 - 12 - 16 = 49

Answer 10

Area of the rectangle mines Four triangles

Answer 11

Find the area of the whole rectangle than subtract each triangles area. Or it is half the area of the rectangle.