All categories

2 years ago

What is the area of the figure ?

Mathematics

2 answers:

nlexa [21]2 years ago

6 0

Answer:

70 cm^2

Step-by-step explanation:

The area of square is 5×10=50 plus the square of triangle, high of triangle is 18-10=8 and base of triangle is 5 because it common base with square, so the square of triangle is 1/2(8)(5)=20

The total area is 50+20=70 cm^2

Gelneren [198K]2 years ago

3 0

Answer: The correct option is (C) 70 cm².

Step-by-step explanation: We are given to find the area of the figure shown in the picture.

We note that the figure is composed of rectangle and a triangle.

The length and width of the rectangle are

l = 10 cm and w = 5 cm.

So, the area of the rectangle is

$A_r=l\times w=10\times5=50~\textup{cm}^2.$

The base (b) of the triangle is 5 cm and the height (h) is

h = 18 - 10 = 8 cm.

So, the area of the triangle is

$A_t=\dfrac{1}{2}bh=\dfrac{1}{2}\times5\times8=20~\textup{cm}^2.$

Therefore, the area of the figure is given by

$A=A_r+A_t=50+20=70~\textup{cm}^2.$

Thus, the required area of the given figure is 70 cm².

Option (C) is CORRECT.

You might be interested in

[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.

miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: $SA=2\pi rh+2\pi r^2$

Volume: $V=\pi r^2h$

Therefore, the height of a cylinder given its volume would be $h=\frac{V}{\pi r^2}$ , thus:

$SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2$

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

$\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r$

$0=-\frac{800}{r^2}+4\pi r$

$0=800\pi+4\pi r^3$

$-800\pi=4\pi r^3$

$-200=r^3$

$r\approx5.848$

If $0If [tex]r>5.848$ , then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is $r=5.848cm$ , making the minimum height $h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm$ .