Plane Geometry

Slides by Engr. Gerard Vincent P. Batusin

Problem 1: Area of Smaller Segment

A circle is divided into two parts by a chord, 3 cm away from the center. Find the area of the smaller part, in cm square, if the circle has an area of 201 cm square.

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Problem 2: Area of a Sector given the Perimeter

Determine the area of a sector of a circle if its perimeter is 19 inches and the radius is 6 inches.

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Problem 3: Central Angle is Twice the Inscribed Angle

A triangle with an area of 90 cm² is inscribed in a 20-cm diameter semi-circle such that its vertices touch the semi-circle. If one side of the triangle measures 20 cm, find the other two sides of the triangle.

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Problem 4: Intersecting Chords

Chord AB and CD intersect at point "O". "AO = 8 cm", "CO = 12 cm", and "DO = 20 cm". If "AB" is the diameter of the circle. Calculate the area "OCA".

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Problem 5: Rectangular Garden (Worded Problem)

The length of a rectangular garden is 9m longer than its width. If the area of the garden is 78.6 square meters, finds its dimensions.

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Problem 6: Cyclic Quadrilateral

The sides of a cyclic quadrilateral measures 8cm, 9cm, 12cm, and 7cm, respectively.
a. Find the area of the cyclic quadrilateral.
b. Find the area of the circumscribing circle.

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Problem 7: Cyclic Quadrilateral Building Site

A building site is in the form of a quadrilateral with following sides and angles given. AB = 52.4 m, BC = 28.5 m, CD = 34.6 m, angle B = 72°, and angle D = 75°. Determine the area of the site.

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Problem 8: Hexagon (Polygon General Formulas)

A regular hexagon whose sides measure 30º each is inscribed in a circle. Determine the following:
a. The number of diagonals
b. The interior angle on each side
c. The radius of the circumscribing circle
d. The length of the apothem
e. The area of the polygon

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