How can we find the area of irregular shapes?

Question

Violet Aldrich · Accepted Answer

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.

HIX Tutor · Answer

undefined Great question! Finding the area of irregular shapes can be fun. Let's think about it step-by-step.

1. **Break It Down**: Can you see if the shape can be divided into smaller, regular shapes? What shapes can you find?

2. **Measure**: For each smaller shape, can you measure the sides or angles? What shapes did you find?

3. **Use Area Formulas**: Do you know the formulas for the areas of those regular shapes? For example:
   - Rectangle: Length × Width
   - Triangle: (Base × Height) ÷ 2
   - Circle: π × Radius²

4. **Calculate**: Can you calculate the area of each smaller shape using the formulas?

5. **Add Them Up**: Once you have the areas, can you add them together? What does that give you?

6. **Check**: Does the total area make sense for the whole shape?

What do you think? How would you start with your shape?

Carson Arnold · Answer

undefined 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.