9514 1404 393
Answer:
9 square units
Step-by-step explanation:
Pick's theorem is a useful relationship in circumstances like these. It tells you the area is ...
A = i + b/2 - 1
where i is the number of interior points (8), and b is the number of points on the border (4).
The area of this figure is ...
A = 8 + 4/2 -1 = 9
The area of the polygon is 9 square units.
_____
You can also get there by realizing the bounding rectangle is 4 units square. From that, corner triangles are cut. CW from upper left, those triangles have (base, height) dimensions of (3, 2), (1, 3), (3, 1), and (1, 2). So, the total of their areas is (1/2)(6 +3 + 3 +2) = 7 square units. The shaded area is then 16-7 = 9 square units, same as above.
Yes, equilateral triangles are 60 degrees unlike right angles that are 90.
<u>Answer:</u>
The height of the tower nearby the pole is 102 m.
<u>Solution:</u>
Given,
Height of the pole = 3.5 m
Length of the shadow of the pole = 1.47 m
Length of the shadow of the tower nearby = 42.75 m
Let us assume the height of the tower as x
On solving for x we get,
On rounding off to the nearest meter we get,
x=102 m
The height of the tower is 102 meter.
Answer:
The solution is ( 1/2 , 5)
Step-by-step explanation:
∵ 8x + 7y = 39 ⇒ (1)
∵ 4x - 14y = -68 ⇒ (2)
Multiply (1) by 2
16x + 14y = 78 ⇒ (3)
Add (2) and (3)
∴ 20x = 10 ⇒ x = 10 ÷ 20 = 1/2
∴ x = 1/2
By substitute in (1)
8(1/2) + 7y = 39 ⇒ 7y = 39 - 4 = 35 ⇒ y = 35 ÷ 7 = 5
∴ y = 5
∴ The solution is ( 1/2 , 5)
To check:
8(1/2) + 7(5) = 4 + 35 = 39 = R.H.S
4(1/2) - 14(5) = 2 - 70 = -68 = R.H.S
