jugoslav

I made an error in the above post. The area of an octagon is NOT 150 cm² !!!  

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Square area is 15² = 225 cm²

Octagon area is 225 - 2(5²) = 175 cm²  

A triangle has three different integer side lengths and a perimeter of 20 units. What is the maximum area of the triangle?

sides are 5, 7, 8       area = 17.321 sq units

Find all 3 sides of the red triangle.

AC = BC = 5    |   ∠ACB = 90º    |    ∠PCQ = 45º    |    ∠ACP = ∠BCQ = 22.5º

Let M be a midpoint of AB

AB = sqrt (AC² + BC²)

PQ = 2 * [tan(PCM) * CM]              ( CM = AM = BM )

AP = BQ = 1/2 (AB - PQ)

13 is 10% of 130

Let ABCD be a parallelogram. We have that M is the midpoint of AB and N is the midpoint of BC. The segments DM and DN intersect AC at P and Q, respectively. If AC = 15 and DN = 35, what is DQ?

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I used the Intercept theorem (Thales's theorem) to calculate the value of DQ.

Line segments DM and DN trisect diagonal AC.

Line segment MN = 1/2(AC)

An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 60 centimeters. What is the number of square centimeters in the area of the octagon?

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The square side is 15 cm, and the side of an octagon is 5 cm.

Octagon area = 8(2.5 * 7.5) = 150 squared centimeters.

The measure of one of the smaller base angles of an isosceles trapezoid is 60 degrees. The shorter base is 5 inches long and the altitude is 3 sqrt 3 inches long. What is the number of inches in the perimeter of the trapezoid?

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The length of the longer base is    2(3√3 / √3) + 5 = 11

The length of the leg(s) is              sqrt[(3√3)² + 3³] = 6

The perimeter is                        P = 5 + 11 + 2*6 = 28 inches ☺

A right circular cone is inscribed in a right prism as shown.  If the right prism is a cube of side length 10, then what is the volume of the cone?

Given that the diagonals of a rhombus are always perpendicular bisectors of each other, what is the area of a rhombus with side length sqrt(10) units and diagonals that differ by 3 units?

side   a = √10

1/2 of shorter diagonal   b = x

1/2 of longer diagonal    c = x + 1.5

a² = b² + c²                   10 = (x + 1.5)² + x²              x = 1.356537443

I'll let you find the area of this rhombus.