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Help me with these Geometry problems please?

0 votes
Round answers to the nearest hundredth, when necessary.

1) Find the area of an equilateral triangle with side lengths of 10 in.

2) Find the perimeter and area of a trapezoid with a height of 12m, legs of 13m, and base lengths of 25m and 35m.

3) Find the area of a parallelogram with a lengths of 16ft and 20ft with two angles of 60 degrees.

5) Find the perimeter and area of a rhombus with side lengths of 35m and a radius of 21m.
asked Jun 17, 2014 in GEOMETRY by anonymous

1 Answer

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(1).The formula for the area of an equilateral triangle A = (√3/4)a2, where a is side length.

The length of the side of equilateral triangle is 10 inches.

The area of an equilateral triangle A = (√3/4)a2 = (√3/4)(10)2 = (√3/4)(100) = 25√3 = 43.3 square inches.

 

(2).The perimeter of a trapezoid P = total of all sides of the trapezoid = 12 + 13 + 25 + 35 = 75 meters.

The area of a trapezoid A = (1/2)*(b₁*b₂)*h, where h is height, b₁ and b₂ are base lengths.

A = (1/2)*(25 + 35)*12 = (1/2)*(60)*12 = 360 square meters.

 

(3)The area of a parallelogram A = base * height.

Find the height : sin θ = opp/hyp ⟹ sin 60 = h/16 ⟹ √3/2 = h/16 ⟹ √3/2 = h/16 ⟹ h = 8√3.

A = 20 * 8√3 = 160√3 = 277.13 square feet.

 

(5).The perimeter of a ramous P = 4*side length = 4(35) = 140 meters.

The area of a ramous A = (1/2)*ab, where a and b are length of the two diagonals.

Length of the one diagonal = 2r₁ = 2(21) = 42 meters.

Find length of the another diagonal :

(35)2 = (21)2 + (r2)2

1225 = 441 + (r2)2

784 = (r2)2

28 = r2.

Length of the another diagonal = 2r2 = 2(28) = 56 meters.

Area of a ramous A = (1/2)*(42)(56) = 1176 square meters.

answered Jun 18, 2014 by casacop Expert

2). The area of a trapezoid A = (1/2)*(b₁ + b₂)*h, where h is height, b₁ and b₂ are base lengths.

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