Answer:
The permimeter is 93 units.
The area is 500 square units
Step-by-step explanation:
Perimeter (image 1, the one with yellow lines)
If we want to find out the perimeter of this hexagon we must sum every side of the shape. The image shows some measurements, but there are some others that are missing.
We already know the following measurements:
AB: 10 units
DE: 10 units
The measurements of BC, CD, EF and FA are missing and if we want to find out these sizes it’s necessary to use Pythagoras theorem.
For BC and CD, we assume that triangles formed with the sides are similar because they have two equivalent sides and an identical angle.
Let’s name these triangles as BCX and CDX,
BX = DX: 10 units
CX: 10 units
Using Pythagoras theorem;
BX² + CX² = BC²
10² + 10² = 200
BC = √200 = 14.14 units
Knowing that BX and DX are identical sides and both of triangles share the CX side, we assume the size of CD is also 14.14 units.
Then, we do the same with triangle formed by EFZ and FAZ
EZ = AZ: 10 units
FZ: 20 units
10² + 20² = 500
FA = EF = √500 = 22.36 units
Summing the sides:
AB + BC + CD + DE + EF + FA
10 units + 14.14 units + 14.14 units + 10 units + 22.36 units + 22.36 units = 93 units
The perimeter of hexagon ABCDEF is 93 units
Area (image 2, the one with red lines)
There isn’t a formula for finding out the area of a hexagon, so we can discover it by splitting this in simple shapes.
After we split the hexagon we can see three shapes, two triangles and one rectangle.
Shape 1: Triangle FAE: The area of a triangle is given by the following formula:
(Base ×Height)/2= (20 units × 20 units)/2= 200 units
Shape 2: Rectangle ABDE: The area of a triangle is given by the following formula:
Base * Height
10 units * 20 units = 200 units
Shape 3: Triangle CBD: We already know the formula.
(20 units × 10 units)/2= 100 units
Then, we sum all of the results.
Area of triangle FAE + Area of rectangle ABDE + Area of triangle CBD
200 units + 200 units + 100 units = 500 units
The area of the hexagon is 500 units.
