Answer:
The area and the perimeter of the picture are:
- Area = 160 cm^2
- Perimeter = 67.31 cm
Step-by-step explanation:
To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:
- Area of a rectangle = base * height
As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:
- Area of a rectangle = 16 cm * 12 cm
- Area of a rectangle = 192 cm^2
Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:
- Area of a triangle = (base * height) / 2
The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:
- Area of a triangle = (8 cm * 8 cm) / 2
- Area of a triangle = (64 cm^2) / 2
- Area of a triangle = 32 cm^2
We subtract to the found area:
- Area of the picture = 192 cm^2 - 32 cm^2
- Area of the picture = 160 cm^2
To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:
- [tex]a^{2}+b^{2}=c^{2}[/tex]
Where:
- a = Opposite leg (8 cm)
- b = Adjacent leg (8 cm)
So, we replace in the theorem:
- [tex]a^{2}+b^{2}=c^{2}[/tex]
- [tex](8 cm)^{2}+(8cm)^{2}=c^{2}[/tex] (and we clear c)
- [tex]\sqrt{(8 cm)^{2}+(8cm)^{2}} =c[/tex]
- [tex]\sqrt{64 cm^{2}+64cm^{2}} =c[/tex]
- [tex]\sqrt{128cm^{2}} =c[/tex]
- c = 11.3137085 cm
- c ≅ 11.31 cm
At last, we add all the sides of the picture begining by the base and going by the left side:
- Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
- Perimeter of the picture = 67.31 cm approximately.
