Help me with these Geometry problems please?

Question

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.

Answer 1

(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.

Comments

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