A shipment of 105 Otter box covers for I-phones has arrived. The total invoice (excluding tax, shipping, etc.) is $3,849.75.
1 answer:
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Problem setup:
The shape is way too complicated by itself, so I cut the shape into 5 different parts.
Please refer to the attached image or my answer will not make much sense.
Shape 1:
This is a triangle. The base is 3 and the height is 2. Thus, the area is:
Shape 1 has an area of 3 square units.
Shape 2:
This shape is also a triangle. The base is 4 and the height is 2. Thus, the area is:
Shape 2 has an area of 4 square units.
Shape 3:
This a unit square (the side lengths are 1).
Thus, Shape 3 has an area of 1 square unit.
Shape 4:
This shape is a rectangle. The base is 3 and the height is 4. Thus, the area is:
Shape 4 has an area of 12 square units.
Shape 5:
This shape is also a rectangle. The base is 4 and the height is 2. Thus, the area is:
Shape 5 has an area of 8 square units.
Total shape:
Add the areas of all 5 shapes to find the area of the shaded figure.
The figure has a total area of 26 square units.
Side notes:
There is a way to solve this problem by only dividing this into only 3 different shapes, can you figure it out?
Let me know if you need a hint or any clarifications, thanks!
~ Padoru
Let's separate the hexagon into 5 shapes; 2 triangles on each side, and a rectangle in the middle. Now let's find the area of each of the smaller shapes.
Top left triangle:
The equation to find the area of a triangle is
(base = b, height = h, a = area)
a = b · h ·
Now let's add in our values and solve.
a = 2 · 4 ·
a = 8 ·
a = 4
Now since there are 4 of these triangles, and they're all the same size,
4 · 4 = 16
All of the triangles put together = 16cm²
The middle rectangle:
The equation to find the area of a rectangle is simple:
(w = width, l = length, a = area)
a = w · l
Now let's put in our values and solve.
a = 4 · 8
a = 32
The rectangle is 32cm²
Now let's add the areas together.
32 + 16 = 48
The answer is <span>48cm²
Hope this helped! If you have anymore questions or don't understand, please comment or DM me. :)
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Top left triangle:
The equation to find the area of a triangle is
(base = b, height = h, a = area)
a = b · h ·
Now let's add in our values and solve.
a = 2 · 4 ·
a = 8 ·
a = 4
Now since there are 4 of these triangles, and they're all the same size,
4 · 4 = 16
All of the triangles put together = 16cm²
The middle rectangle:
The equation to find the area of a rectangle is simple:
(w = width, l = length, a = area)
a = w · l
Now let's put in our values and solve.
a = 4 · 8
a = 32
The rectangle is 32cm²
Now let's add the areas together.
32 + 16 = 48
The answer is <span>48cm²
Hope this helped! If you have anymore questions or don't understand, please comment or DM me. :)
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