Question

What will be the area of the given shape? (please help)

Answer 1

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Answer:  $\textsf{620 units squared}$

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Given: $\textsf{Side lengths = 10, 12, 14, 14, 10, 12}$

Find: $\textsf{The area of the shape}$

Solution:  We need to split this shape into several different rectangles and once we find the area for each individual one we can combine them to get the total area.

Determine the area of the rectangle going down

• $A_{vertical}\textsf{ = l * w}$

• $A_{vertical}\textsf{ = 10 * (12 + 10 + 12)}$

• $A_{vertical}\textsf{ = 10 * 34}$

• $A_{vertical}\textsf{ = 340}$

Determine the area of the left rectangle

• $A_{left}\textsf{ = l * w}$

• $A_{left}\textsf{ = 14 * 10}$

• $A_{left}\textsf{ = 140}$

Determine the area of the right rectangle

• $A_{right}\textsf{ = l * w}$

• $A_{right}\textsf{ = 14 * 10}$

• $A_{right}\textsf{ = 140}$

Determine the total area

• $A_{total} = A_{vertical} + A_{left} + A_{right}$

• $A_{total}\textsf{ = 340 + 140 + 140}$

• $A_{total}\textsf{ = 620}$

Therefore, the total area of the given shape would be 620 units squared.

Answer 2

Answer:

620

Step-by-step explanation:

To find the area of strangely-shaped structures, like this one, it is easiest if we cut the shape into smaller, more recognizable, shapes..

We can first cut off the top/center rectangle of this shape , which has a width of 10, and a length of 12. The "area" is length × width.

So, we multiply 12 × 10 to find the area of this section.

12 × 10 = 120

if we look at the bottom half, we can see that there is an identical rectangle (because it has the same width of 10 and length of 12) ! So, we can simply add 120 to our total twice to count both of these areas.

(when putting areas of multiple portions together, we add--not multiply)

  120 (first/top rectangle)

+ 120 (lower rectangle)

_______________

   240

So, our area so far is 240.

Now, we need to find the horizontal (left-right) section of this shape.

We can see that it has a width of 10 (look at the right end), and a length of 38      14 + 10 + 14 (38 total)

So, to find the area of this portion, we will multiply its length × width, which we know is: 38 × 10

38 × 10 = 380.

So, we can now add our areas together:

  240

+ 380

__________

  620

So, our area of this shape is 620