Question

(High points) please solve with explanation

Answer 1

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:

• $a^{2}+b^{2}=c^{2}$

Where:

• a = Opposite leg (8 cm)
• b = Adjacent leg (8 cm)

So, we replace in the theorem:

• $a^{2}+b^{2}=c^{2}$

• $(8 cm)^{2}+(8cm)^{2}=c^{2}$ (and we clear c)
• $\sqrt{(8 cm)^{2}+(8cm)^{2}} =c$
• $\sqrt{64 cm^{2}+64cm^{2}} =c$
• $\sqrt{128cm^{2}} =c$
• 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.