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4 years ago

What is the volume and surface area of this triangular prism?

Mathematics

1 answer:

bija089 [108]4 years ago

8 0

For volume you multiply length by width.

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please help me, Prove a quadrilateral with vertices G(1,-1), H(5,1), I(4,3) and J(0,1) is a rectangle using the parallelogram me

mestny [16]

Answer:

Step-by-step explanation:

We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).

Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus

Join JH and GI such that they form the diagonals of the quadrilateral.Now,

JH= $\sqrt{(5-0)^{2}+(1-1)^{2}}=5$ and

GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$

Now, mid point of JH= $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

= $(\frac{5+0}{2},\frac{1+1}{2})=(\frac{5}{2},1)$

Mid point of GI= $(\frac{5}{2},1)$

Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.

Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.

Thus, From ΔGIJ, we have

$(GI)^{2}=(IJ)^{2}+(JG)^{2}$ (1)

Now, JI= $\sqrt{(4-0)^{2}+(3-1)^{2}}=\sqrt{20}$ and GJ= $\sqrt{(0-1)^{2}+(1+1)^{2}}=\sqrt{5}$

Substituting these values in (1), we get

$5^{2}=(\sqrt{20})^{2}+(\sqrt{5})^{2} }$

$25=20+5$

$25=25$

Thus, GIJ is a right angles triangle.

Hence, GHIJ is a rectangle.

Also, The diagonals GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$ and HJ= $\sqrt{(0-5)^2+(1-1)^2}=5$ are equal, thus, GHIJ is a rectangle.

6 0

3 years ago

Complete the proof that ∠PST≅∠QRT. S P Q R T

EastWind [94]

Answer: Transitive property of congruence

3 0

3 years ago

Read 2 more answers

Find the area of the polygon:

Darya [45]

Answer:

Step-by-step explanation:

o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

8 0

3 years ago

the width of a laptop is 11.25 inches. the width is 0.75 times the length. what is the length of the laptop

Snezhnost [94]

$\bf \stackrel{width}{11.25}=0.75\stackrel{length}{L}\implies \cfrac{11.25}{0.75}=L\implies 15=L$

8 0

3 years ago

Please Help ASAP If you want brainliest and 5 fives and thanks and friends list

neonofarm [45]

Answer: 22 miles

Step-by-step explanation:

1/4 times 4 = 1 gallon

if Rob can travel 5 and 1/2 miles on 1/4, then to find how far he can travel on 1 gallon we multiply 51/2 by 4

5 1/2 x 4 = 22

4 0

3 years ago