The lateral area of the prism is given by:
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2
The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2
For example, lets say:
L = 10
H = 6
W = 4
Imagine the shape is facing slightly towards your left
A left vertical cross section (perpendicular to the base) of the cuboid would result in a 10 by 6 rectangle
A right vertical cross section (perpendicular to the base) of the cuboid would result in a 6 by 4 rectangle
A horizontal cross section (parallel to the base) of the cuboid would result in a 10 by 4 rectangle
An angled cross section (through the middle) would also give a rectangle but the dimensions would be different. If the cut went from one '4' edge to the one in the opposite corner, the length of that would be found using Pythagoras
a² + b² = c²
6² + 10² = c²
36 + 100 = 136
√136 ≈ 11.66cm
11.66 by 4 rectangle
The shows that the resulting shape will always be a rectangle for these cross sections.
<em>The only case in which it would not, would be if one of the faces of the cuboid was a square - in which case one of the cross sections would also be a square.</em>
9514 1404 393
Answer:
∠6 = ∠4 = 84°
∠5 = ∠3 = 96°
Step-by-step explanation:
Angle 4 and the marked angle (84°) are <em>corresponding</em> angles, so are congruent. Angles 4 and 6 are vertical angles, so are congruent.
∠6 = ∠4 = 84°
Angle 3 and the marked angle are a linear pair, so angle 3 is the supplement of 84°:
∠3 = 180° -84° = 96°
Angle 3 and angle 5 are <em>alternate interior </em>angles, so are congruent.
∠5 = ∠3 = 96°
For #2 you would count how many where the red dashed line is! Which is 3! Then you would count where the blue dashed line is! Which is 4! So then it would be 4/3(4 over 3) For the slope! Hope this helps! :)
