Geometry help?

When trying to find the area of a shape, try splitting it up into shapes we can easily calculate the area for, triangles and rectangles.

The best choice here would be to split the shape into a rectangle with lengths 4 and 8, and then triangle we have on top.

So the area of the rectangle is 4 x 8 = 32.

The area of a triangle is equal to 1/2 x base x height, so we need to find the height.

Because the triangle we have is an isosceles triangle with lengths 5, 5 and 8, we can split it directly down the middle to form two right angle triangles.

So the base of one of these is 4, the hypotenuse is 5 and we are left with the side corresponding to the height of the triangle.

Using Pythagoras' theorem, a^2 + b^2 = c^2, we can calculate the missing length.

4^2 + b^2 = 5^2

16 + b^2 = 25

b^2 = 9

Hence b = 3.

So the area of the original triangle, (before we split it into two), is

1/2 x 8 x 3 = 12.

So the area of the whole shape is 32 + 12 = 44 (sq units).

See the picture below to view a diagram.

Note: Area = perimeter • apothem ÷ 2 only works for regular polygons (all sides equal and angle measures equal) so it won't work on this example.

Divide it into two shapes. A rectangle with sides 8 and 4 and an isosceles triangle with base 8 and height 3

Area = 8 x 4 + 1/2 x 8 x 3

= 32 + 4 x 3

= 32 + 12

= 44 sq units