6. Isosceles trapezoid SAND has diagonals SN = 5w + 13 and AD = 11w

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

3 years ago

My math teacher told me that circumstance was pie I dont know what pie is ;(

agasfer [191]

Answer:

Pie= 3.14

Step-by-step explanation:

The enclosing boundary of a curved geometric figure, especially a circle.The circumference = π x the diameter of the circle (Pi multiplied by the diameter of the circle). Simply divide the circumference by π and you will have the length of the diameter. The diameter is just the radius times two, so divide the diameter by two and you will have the radius of the circle!

3 0

3 years ago

Read 2 more answers

A box contains 4 oranges, 9 apples, and 3 pears. Liliana selects a piece of fruit from the box at random. What is the probabilit

valina [46]

Hello!

You first find out how many objects there are in total

4 + 9 + 3 = 16

Then you find the probability of Liliana picking a orange

Since there are 4 oranges and 16 things to pick she has a 4/16 chance of getting an orange

Next you find the probability of Liliana picking a pear

There are 3 pears and 16 items to pick so she has a 3/16 chance

Then you add them together to find the chance of either happening

4/16 + 3/16 = 7/16

So she has a 7 out of 16 chance of getting an orange or a pear

The answer is 7/16

Hope this helps!

3 0

3 years ago

The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic s

Valentin [98]

Answer:

Larger number:

16

Smaller number

3

Step-by-step explanation:

Larger number: 16

Smaller number: 3

Explanation:

Suppose the larger number is

a

and the smaller number is

b

.

You solve the following system of equations:

a⋅b=48

a−13=b

Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48

a 2−13a=48

a2−13a−48=0

Factor the polynomial:

(a−16)(a+3)=0

a=16 or a=−3a is positive so a=16.

We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.

5 0

3 years ago

Use the graph to find the value of the function f(<img src="https://tex.z-dn.net/?f=%20%5Cpi%20" id="TexFormula1" title=" \pi "

SSSSS [86.1K]

Hi my name is jeff 5.000325

8 0

3 years ago

6. Isosceles trapezoid SAND has diagonals SN = 5w + 13 and AD = 11w - 5. . Determine the value of w.​

6. Isosceles trapezoid SAND has diagonals SN = 5w + 13 and AD = 11w - 5. . Determine the value of w.