Come on. First, you need the area of the cross section which is a trapezium. How do you find the area of a trapezium?
Post what you get. We'll try to continue from there.
Come on. First, you need the area of the cross section which is a trapezium. How do you find the area of a trapezium?
Post what you get. We'll try to continue from there.
For the volume, the two edges are identical.
You can cut one off and place it on top of the other.
This gives you a rectangular block of sides 11, 20, 4.
The surface area of the front and back sides can be calculated from there.
Going back to your original drawing, the other sides are 8 by 20, 5 by 20, 14 by 20.
It should be the exact same as the area of a rectangle + the area of 2 identical triangles,
which is 4(8)+2(0.5)(3)4=32+12.
The volume is simplest if you make an 11 by 4 by 20 block, which is 11 by 80 cubic units.
Otherwise, simply multiply base area by height,
or front face area by depth, whichever way you want to look at it.
So, 44 by 20 is ?
The surface area is the number of "unit squares" you could place on the surface.
A unit square has all 4 sides equal to 1 unit in length.
The surface area of such a square is 1 square unit.
If you have a rectangular floor 10 meters by 5 meters, how many tiles of surface area 1 square meter
could you tile the floor with?
You'd have 10 rows of 5 right?
Or 5 rows of 10, so you multiply 5 by 10.
Of course, the corners need to be right-angles.
However, that's the basis of calculating surface area.
In your shape, if you cut off one of the triangular edges and place it upside-down on the other edge,
you will have a rectangular front face of sides 11 and 4 units.
Therefore, how many unit squares will be on that face ?
44 right?
Alternatively, a right-triangle is half a rectangle,
so we can add up the areas of the two triangles and the rectangle in between.
Surface area is measured in square units.
For volume, think in terms of cubes (such as ice cubes or sugar cubes)
that have all sides 1 unit in length.
If you have a box of sides 5cm, 2cm and 3cm,
how many 1 cm sugar cubes could you get inside?
There will be 5(2)=10 lined up against one face and there will be 3 such rows.
That's why you multiply all three numbers.
The units will be cubic units.
volume = [8 x 4 + 2(0.5 x 4 x 3)] x 20
= ( 32 + 2 x 6) x 20
= ( 32 + 12) x 20
= 44 x 20 = 880 cube units
surface area = (3 + 8 +3) x 20 + 8 x 20 + 2 x (5 x 20) + 2 x 8 x 4 + 4 x (0.5 x 4 x 3)
= 14 x 20 + 160 + 2 x 100 + 64 + 4 x 6
= 280 + 160 + 200 + 64 + 24
= 728 square units.