Will give brainliest and please show work

Mathematics

2 answers:

Tcecarenko [31]3 years ago

8 0

Let us break this figure into smaller shapes.

If you notice there are 4 small right triangles, one at each corner of the shape.
There are 2 small rectangles, one on the top and one on the bottom.
There is 1 big rectangle sitting in the middle.

One trick we can do to calculate the area faster is instead of saying 4 small triangles, we can say there are 2 small squares.
The reason we can do this is because all the triangles have a base length of 2 and a height of 2 also. If we put two triangles together they form a rectangle or square, but in this case it forms a square.

Now let's find the area of each of the small parts: small square, small rectangle, and big rectangle.
Remember: Area of rectangle = length x width.

Area of 1 small square (made of two small triangles): It has a length of 2 units and a height of 2 units so each square's area is, 2 x 2 = 4 square units

Area of 1 small rectangle: It has a width of 2 units and a length of 6 units. The rectangle's area is 2 x 6 = 12 square units

Area of big rectangle: It has a width of 6 units and a length of 8 units. This means the big rectangle's area is 6 x 8 = 48 square units.

To find the area of the whole figure we add up all the small parts.

Area of 1 small square: 4 square units
Area of 1 small rectangle: 12 square units
Area of 1 big rectangle: 48 square units.

Note: We have 2 small squares, 2 small rectangles, and 1 big rectangle.

Total area of whole figure = 2(area of small square) + 2(area of small rectangle) + 1(area of big rectangle)

Total area of the figure is 80 square units.