Answer:
1.) 49.5 mm ^2
2.) 183 in. ^ 2
Step-by-step explanation:
So for number one, it's a very irregular shape, but luckily, we can split it vertically! Into a triangle & a quadrilateral.
The area of the quadrilateral would be
6*7 = 42
The triangle is more difficult, because its not directly given, BUT, we do know that the height would have to be 6 minus 3, and the base would be 12 minus 7... So the equation is
[tex]A = \frac{1}{2} bh\\A = \frac{1}{2}(5)(3)\\A = 7.5[/tex]
Now, the rectangle and the triangle account for the total area in this case, when you add them, you get 49.5 mm ^2
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For the second, we have a trapezoid with a triangular cutout, the area of a trapezoid is defined as:
[tex]A = \frac{1}{2} (B1-B2) h[/tex]
Luckliy, none of the numbers of the bases, or height, are hidden. The height is 18, the larger base is 51, and the smaller is 24.
[tex]A = \frac{1}{2} (51-24)18\\A = 243[/tex]
So, the trapezoid area is 243 in ^2. But we aren't done, we still have the triangle! It will be easy though!
Remember, the formula for a triangle is half the base times the height. These numbers are directly given to us!
[tex]A = \frac{1}{2} (12)(9)\\A = 54[/tex]
Now, since the triangle is NOT SHADED, we subtract it's area from the trapezoid's...
[tex]243 - 54 = 183[/tex]
The area is 183 in. ^ 2
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