Find the area of the shaded segment. Round your answer to the nearest square centimeter. 24 cm2 23 cm2 21 cm2 22 cm2
1 answer:
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Question:
Find the area of the shaded segment. Round your answer to the nearest square centimeter.
a) 24 cm²
b) 23 cm²
c) 21 cm²
d) 22 cm²
Answer:
d) 22 cm²
Step-by-step explanation:
We have Area and a Triangle in that diagram.
In other to find the shades segment , we have to find the Area of the triangle and the Area of the sector
Step 1
Area of a Triangle
= 1/2 × a × b × sin θ
Where θ = 120°
a = 6 cm
b = 6 cm
Area of the triangle = 1/2 × 6 × 6 × sin 120°
= 15.59 cm²
Step 2
Area of the sector
The formula is given as
Area = πr²θ/360
r = radius = 6cm
Area = π × 6² × 120/ 360
Area = 37.699111843cm²
Approximately = 37.70 cm²
Step 3
The Area of the shaded segment = Area of the sector - Area of the triangle
= 37.70cm² - 15.59cm²
= 22.11 cm²
Approximately to the nearest square centimeter
= 22 cm²
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Answer:
45 square inches
Step-by-step explanation:
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom
Total surface = surface area of the base square + area of 4 triangles
Calculate the surface area of the base square
surface area of the square = s^2
where s= side length
s=3 in
The surface area of the base =s^2
=3^2
= 9 square inches
The surface area of the side triangles
The area of the triangle = (1/2)* side length* slant height
Side length=3 in
Slant height=6 in
substituting the values,
The area of the triangle =1/2*3*6
= 18/2
= 9 square inches
There are 4 triangles
The area of 4 triangles = 4 x 9
= 36 square inches
Therefore,
Total surface = surface area of the base square + area of 4 triangles
= 9 + 36
= 45 square inches
