# How can we find the area of irregular shapes?

Please see below.

To find the area of an irregular shape, there coud be two ways.

One, if shape is a polygon made using all straight lines. Just join the two farthest points (we will call this line the diagonal) and now draw perpendiculars from other points on to this diagonal. The figure is then divided into tiangles and trapeziums. and we can find its area.

Two, if the shape is not made using straight lines. Then we impose graph on it. Now we can find its area by counting the squares falling in the region covered by the shape. First we count squares completely covered and then we approximate area of partially covered squares, by counting say more than half covered, less than half covered. When everything is added, we get approximate area of the irregular shape.

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To find the area of irregular shapes, you can use one of several methods depending on the shape. For shapes with straight sides, you can divide the shape into smaller, simpler shapes (like triangles, rectangles, or squares), find the area of each smaller shape, and then add them together to get the total area of the irregular shape. For shapes with curved sides, like circles, you can use an approximation method like breaking the shape into smaller straight-sided shapes or using calculus if you need a more precise answer.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A chord with a length of #8 # runs from #pi/12 # to #pi/8 # radians on a circle. What is the area of the circle?
- The base of a triangular pyramid is a triangle with corners at #(3 ,7 )#, #(1 ,4 )#, and #(4 ,2 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?
- Two corners of an isosceles triangle are at #(1 ,7 )# and #(5 ,3 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?
- Two corners of an isosceles triangle are at #(4 ,2 )# and #(1 ,3 )#. If the triangle's area is #2 #, what are the lengths of the triangle's sides?
- What kind of shape has vertices #A(-1, -4), B(1, -1), C(4,1), D(2, -2)#?

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