Right triangles 1-2 and 3 are given with all their angle measures and approximate side lengths.

Mathematics

2 answers:

Harman [31]3 years ago

5 0

Answer:

0.34

Step-by-step explanation:

NNADVOKAT [17]3 years ago

3 0

Answer: 0.34

Step-by-step explanation: Khan Academy

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alexdok [17]

Note that no diagram is drawn to scale.

If the diagram in the first picture is further worked upon, we have polygon ABCDE.

Note also that line AD = 18in and line MD = 10in.
This simply means the line Am = AD - MD = 8in.

We have the height of the triangle needed to solve for the area of the triangle. Area of Triangle = 1/2×b×h
Where b is length base of the triangle and h is the length of height of the triangle.
We still need b to find the Area.

Note also that two opposite sides of parallelograms are equal. This implies that line DC = line EB which is equal to 14in.
In the third image, you can see this. Half the length of the side of the parallelogram is needed. This means 14/2 = 7in.

We can now solve for the Area of the triangle.
$Area = \frac{1}{2} (b \times h)$
$Area = \frac{1}{2} (7 \times 8)$
$Area = 28$
We have the are of the triangle to be 28in. Multiply this by 3 to find the total area of all three triangles since the three triangles are identical. Thus,
Total Area of all Triangles = 28×3 = 76in

Now, find the area of the two parallelograms.
Area of parallelogram EBCD = bh

Where b is the length of the base side and h is the height.
Hence from the diagram,
$Area = 14 \times 10 \\ Area = 140$
Area of parallelogram EBCD is 140in.

Total Area of both Parallelograms will be 140 ×2= 280in since both are identical.

To find the Total Area of the tile pattern add the area of the triangles and the Parallelograms. This is 76 + 280 =356in.

Your answer is 356in.