I running track is 400 meters. if i make 4 laps, what is the distance that i traveled?

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

4 0

2 years ago

Which of the following points are solutions to the system of inequalities shown below?

pychu [463]

This is easy, love. It's E

3 0

2 years ago

Read 2 more answers

What is the solution to the system of equations?<br>- (8. –1)<br>0 (s. 2)<br>19 (3:5)

Oksana_A [137]

Answer:

Step-by-step explanation: You have to do the distributive property to get the answer.

3 0

3 years ago

If this trapezoid is moved through the

miskamm [114]

Hi! I'm happy to help!

We can see that A's coordinates currently are -6 for x and 2 for y.

When we move x+3, it moves the x coordinate to the right 3 units. This changes it from -6 to -3. When we move y -2, we move the y coordinate down 2 units. This changes it from 2, to 0.

To sum it up: The final coordinates of A will be -3 for x and 0 for y, also written as (-3,0).

I hope this was helpful, keep learning! :D

7 0

2 years ago

David purchased some cookies at the cost of 5 for $4 and sold them at 4 for $5. David made a profit of $180 in total. How many c

horsena [70]

David purchased some cookies at the cost of

5 for $4 (5/4=1.25) and

sold them at 4 for $5(4/5=0.80).

To find cost per cookie subtract 1.25-0.80=0.45

David made a profit of $180 in total ( divide profit per cookie cost: 180/0.45= 400)

How many cookies did David purchase to make that much money?

He needed to make 400 cookie to make the profit of $180.

5 0

2 years ago