Mathematics, 01.08.2019 01:00 ghwolf4p0m7x0

Aright triangular prism is shown. find (a) the total surface area and (b) the volume. you must show formulas and your work. 10m height 8m width 10.77m

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Hello!

We are going to use the rectangular prism of the image as a guide:

First of all, the AC segment is calculated using the Pythagoras' theorem:

$AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m$

(A) The surface area of a prism is the sum of the surface areas of each face.

For the 2 triangles ABC and DEF

A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m

For the ABEF Rectangle

$A=w*l=10,77m*10m=107,7m^{2}$

For the ACDE Rectangle

$A=w*l=10,77m*12,81m=137,96 m^{2}$

For the BCDF Rectangle

$A=w*l=10,77m*8m=86,16 m^{2}$

To finish you need to sum up the areas of each face:

$SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2}$

(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows

$V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3}$

Aright triangular prism is shown. find (a) the total surface area and (b) the volume. you must show

Aright triangular prism is shown. find (a) the total surface area and (b) the volume. you must show

Answer from: Quest

18a

step-by-step explanation:

simply because it is. it's the highest common factor

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Aright triangular prism is shown. find (a) the total surface area and (b) the volume. you must show...

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