jugoslav

Trapezoid area    A = √1,199,055   

In triangle PQR, PQ=13, QR=14, and PR=15. Let M be the midpoint of QR. Find PM.

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PM = 1/2 [sqrt(2*15² + 2*13² - 14²)]

PM = 2√37

Let XY be a tangent to a circle, and let be an XBA secant of the circle, as shown below. If AX = 16 and XY = 8, then what is AB?

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XY² = XB * AX

8² = XB * 16

XB = 4            AB = 12

This is a flat pattern of the part from the original diagram.

Red dotted lines are bend lines.

NQ = NP = sin30º * 120            NQ = 60

Angle x = 50 degrees

The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid have a length of 28, and the two diagonals of the trapezoid have a length of 52. What is the area of the trapezoid?

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Height      h = sqrt(28² - 15²) 

Shorter Base      SB = sqrt(52² - h²) - 15

Longer Base      LB = SB + 30

Trapezoid area       A = 1/2 (SB + LB) * h

[CBOQ] = 2.75 square units

CB = 1.25          ∠CBO ≅ ∠HOB

∠COB = 2(sin^-1(BM / OB))

∠CBO = ∠HOB = 1/2(180 - ∠COB)

∠COH = ∠COB + ∠HOB

CH = 2*[sin(COH /2) * OH] 

Line segment CH = 7.5 units (!!!) 

Let ABCD be a square. Three parallel lines x,y, and z pass through A, B, and C respectively. The distance between x and y is 4 and the distance between y and z is 5. Find the area of the square.

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Area = 4² + 5² = 41 square units