geometry homework!!!!

Question

1) An equilateral triangle has a side length os 2/3. Find its area.

2) A square is inscribed in a circle of radius 3/2. Find the area of the square.

3) Triangles A B C and triangle A' B' C' are similar triangles with A' B'/A B = 5/4. If the area of triangle A B C is 80square units, find the area of triangle A' B' C'.

Answer 1

1).

Area of equilateral triangle(A) = (√3 * a²)/4, where a is the side length of equilateral triangle.

Here, a = 2/3.

Area(A) = (√3 * (2/3)²)/4

= (√3 * (4/9))/4

= (√3 * 4)/(4 * 9)

= √3/9

= 1.732/9

= 0.192 square units.

Therefore, area of the equilateral triangle is 0.192 square units.

Answer 2

2).

From the given data, draw a geometric diagram.

Where, radius of the circle is equals to diagonal of the square.

So, r = d = 3/2.

Area of the square(A) = (1/2)d².

= (1/2))(3/2)²

= (1/2) * (9/4)

= 9/8

= 1.13 square units.

Therefore, area of the square is 1.13 square units.

Answer 3

3).

If A'B'/AB =5/4

Then the Area of triangle A'B'C'/Area of ABC = 25/16 (since the area must be something square).

Set x as area of triangle A'B'C'.

We have x/80 =25/16.

x = (25 * 80)/16

x = 125 square units.

Therefore, area of triangle A'B'C' is 125 square units.