GEOMETRY HELP! AREA OF POLYGONS!?
1. Find the area of a regular hexagon with a 48-inch perimeter.
Which multiple choice answer?
48√3 in²
96√3 in²
192√3 in²
2.Find the area of an equilateral triangle with a side of 6 inches.
Which multiple choice answer is it?
9√3 in²
6√3 in²
4.5√3 in²
3. Two polygons are similar with the longest side of one 8 and the longest side of the other 10. Find the ratio of the areas.
Which multiple choice answer is it?
4/5
81/100
16/25
4. An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.
Which multiple choice answer is it?
42 sq. units
21√2 sq. units
21 sq. units
5. Find the area of a regular pentagon with side equal to 3 and apothem equal to K.
Which multiple choice answer is it?
1.5K
7.5K
12K
6. Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
Which multiple choice answer is it?
72√3 sq. units
36√3 sq. units
12√3 sq. units
THANKS SO MUCH!
Answers & Comments
Verified answer
The area of an equilateral triangle is (1/2)(x)(x/2 sqrt 3) = x^2 /4 *sqrt 3 when each side is x.
1. 8 inch sides. 6 equilateral triangles. 6*8^2 /4 *sqrt 3 = 96 sqrt 3.
2. 6^2 /4 sqrt 3 = 9 sqrt 3.
3. (8/10)^2 = 64/100 = 16/25.
4. The height is sqrt(3^2 +3^2) = sqrt 18 = 3 sqrt 2. The area is 7*3 sqrt 2 = 21 sqrt 2.
5. Five triangles with base 3 and height k: 5(1/2*3*k) = 7.5k.
6. The height perpendicular to the sides of length 12 is 3 sqrt 3 and the area is 36 sqrt 3.