Two sides of a triangle measure 8 cm and 12 cm. Find its area if its perimeter is 26cm?

If three sides of an acute triangle is 3cm, 4cm, and “x” cm, what are the possible values of x?

In triangle ABC, AB = 8m and BC = 20m. One possible dimension of CA is?

In a triangle BCD, BC = 25m and CD = 10m. The perimeter of the triangle may be?

The sides of a triangle ABC are AB = 25cm, BC = 39cm, and AC = 40cm. Find Its area?

The corresponding sides of two similar triangles are in the ratio 3:2 what is the ratios of their areas?

Find the area of the triangle whose sides are 12, 16, and 21 units

The sides of a right triangle are 8, 15, and 17 units if each side is doubled, how many square units will be the area of the new triangle

Problem 12-10: The two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less. What is the difference in their areas?

Problem 12-11: A triangular piece of wood having a dimension of 130cm, 180cm, and 190cm is to be divided by a line bisecting the longest side drawn from its opposite vertex. The area of the part adjacent to the 180cm side is?

Find EB if the area of the inner triangle is ¼ of the outer triangle as shown. AC = 65, AD = 45, AB = 90

A piece of wire is shaped to enclose a square whose area is 169cm². It is then reshaped to enclose a rectangle whose length is 15cm. The area of the rectangle is?

The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is 4.5m. What is the area of the room?

A man measuring a rectangle “x” meters by “y” meters, makes each side 15% too small. By how many percent will his estimate for the area be too small?

Problem 12-16: The length of the side of a square is increased by 100%. Its perimeter is increased by:

A piece of wire of length 52cm is cut into two parts. Each part is then bent to form a square. It is found that total area of the two squares is 97 Sq. Cm. The dimension of the bigger square is:

In the figure shown, ABCD is a square and PDC is an equilateral triangle. Find.

One side of a parallelogram is 10m and its diagonals are 16m and 24m respectively. Its area is:

If the sides of the parallelogram and an included angle are 6, 10 and 100 degrees respectively, find the lengths of the shorter diagonal.

The area of a rhombus is 132 square cm. If its shorter diagonal is 12cm, the length of the longer diagonal is:

The diagonals of a rhombus are 10cm and 8cm respectively. Its area is:

Given a cyclic quadrilateral whose sides are 4cm, 5cm, 8cm, and 11cm. Its area is:

A rectangle ABCD which measures 18 by 24 units is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

The sides of a quadrilateral are 10m, 8m, 16m and 20m respectively. Two opposite interior angles have a sum of 225°. Find the area of the quadrilateral in Sq. M.

A non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. Find the ratio of the area of the rectangle to the area of the square.

A trapezoid has an area of 36m² and altitude of 2m. Its two bases in meters have ratio of 4:5, the bases are:

Determine the area of the quadrilateral ABCD shown if OB = 80cm, OA = 120cm, OD = 150cm and θ = 25°.

Problem 12-29: A corner lot of land is 35m on one street and 25m on the other street. The angle between the two lines of the street being 82°. The other two lines of the lot are respectively perpendicular to the lines of the streets. What is the worth of the lot if its unit price is P2500 per square meter?

Determine the area of the quadrilateral having (8, -2), (5, 6), (4, 1), and (-7, 4) as consecutive vertices.

Find the area of the marked portion shown, if AB is parallel to CD.

The deflection angles of any polygon has a sum of:

Problem 12-33: The sum of the interior angles of a dodecagon is:

Each interior angle of a regular polygon is 165°. How many sides?

The sum of the interior angles of a polygon is 540°. Find the number of sides.

The sum of the interior angles of a polygon of n sides is 1080°. Find the value of n.

How many diagonals does a pentadecagon have?

A polygon has 170 diagonals. How many sides does it have?

A regular hexagon with an area of 93.53 square centimeters is inscribed in a circle. The area in the circle not covered by the hexagon is:

The area of a regular decagon inscribed in a circle of a 15cm diameter is:

The sum of the interior angle of a polygon is 2,520°. How many are the sides?

Problem 12-42: The area of a regular hexagon inscribed in a circle of radius 1 is:

The corners of a 2-meter square are cut off to form a regular octagon. What is the length of the sides of the resulting octagon?

If a regular polygon has 27 diagonals, then it is a:

Problem 12-45: One side of a regular octagon is 2. Find the area of the region inside the octagon.

A regular octagon is inscribed in a circle of a radius 10. Find the area of the octagon.

Lot ABCDEFA is a closed traverse in the form of a regular hexagon with each side equal to 100m. The bearing of AB is N 25° E. What is the bearing of CD?

Two sides of a parallelogram measure 68cm and 83cm and the shorter diagonal is 42cm. Determine the smallest interior angle of the parallelogram.

Problem 12-49: The parallel sides of a trapezoidal lot measure 160m and 240m and are 40m apart. Find the length of the dividing line parallel to the two sides that will divide the lot into two equal areas.

What do you call a Polygon with 35 diagonals?

In the figure shown OA and OB are tangent to the circle. If

In the figure shown, arc BC is half the length of arc CD. Solve for Ø.

In the figure shown, MAN is a tangent to the circle of center O. If

In the figure shown, AB is the diameter of the circle. Find angle Ø.

The area of a circle is 89.42 square inches. What is the circumference?

Find the area for the circle shown.

A circle whose area is 452 cm square is cut into two segments by a chord whose distance from the center of the circle is 6 cm. Find the area of the larger segment in cm square.

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.

A quadrilateral ABCD is inscribed in a semi-circle with side AD coinciding with the diameter of the circle. If sides AB, BC, and CD are 8 cm, 10 cm, and 12 cm long, respectively, find the area of the circle.

A semi-circle of radius 14 cm is formed from a piece of wire. If it bent into a rectangle whose length is 1 cm more that its width, find the area of the rectangle.

Find the area of the shaded circle shown.

The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

A sector has a radius of 12 cm. If the length of its arc is 12 cm, its area is:

The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector?

Find the area of the shaded portion.

A swimming pool is to be constructed in the shape of partially overlapping identical circles. Each of the circles has a radius of 9 m, and each passes through the center of the other. Find the area of the swimming pool.

Given are two concentric circles with the outer circle having a radius of 10 cm. If the area of the inner circle is half of the outer circle, find the border between the two circles.

A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle concentric to this circle and tangent to the given chord.

A reserved curve on railroad track consists of two circular arcs. The central angle of one side is 20° with radius 2500 feet, and the central angle of the other is 25° with radius 3000 feet. Find the total lengths of the two arcs.

Given a triangle whose sides are 24 cm, 30 cm, and 36 cm. Find the radius of a circle which is tangent to the shortest and longest side of the triangle, and whose center lies on the third side.

Find the area of the largest circle that can be cut from a triangle whose sides are 10 cm, 18 cm, and 20 cm.

The diameter of the circle circumscribed about a triangle ABC with sides a, b, c is equal to:

The sides of the triangle are 14 cm, 15 cm, and 13 cm. Find the area of the circumscribing circle.

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm.?

If the radius of the circle decreased by 20%, by how much is its area decreased?

The distance between the center of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. The area of the largest circle is.

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

The wheel of a car revolves n times, while the car travels x km. The radius of the wheel meter is:

If the inside wheels of a car running a circular tank are going half as fast as the outside wheel, determine the length of the track, described by the other wheels, if the wheels are 1.5 m apart.

A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft and the goat can reach 1 ft farther than the rope length, what is the maximum area the goat can cover?

What is the area of the shaded portion shown?

The interior angles of a triangle measures 2x, x + 15, and 2x + a. What is the value of x?

Two complementary angles are in the ratio 2:1. Find the larger angle.

Two transmission towers 40 feet high is 200 feet apart. If the lowest point of the cable is 10 feet above the ground, the vertical distance from the roadway to the cable 50 feet from the center is:

What is the area bounded by the curves y² = 4x and x² = 4y?

What is the area between y = 0, y = $$3x^2$$ , x = 0, and x = 2?

A circle having an area of 224 sq. m. is inscribed in an octagon. Find the area of the octagon.

A circle is circumscribed about a hexagon. Determine the area of the hexagon if its area outside the hexagon but inside the circle is 15 sq. cm.

A circle of radius 8 cm is inscribed in a sector having a central angle of 80°. What is the area of the sector?

A triangular piece of land has one side measuring 2 km. The land is to be divided into two equal areas by a dividing line parallel to the given side. What is the length of the dividing line?

A piece of wire having a total length of 72 cm was cut into two unequal segments and bent to form two unequal squares. If the total area of the squares is 180 sq. cm, what is the difference in the lengths of the two segments?

Determine the area of a regular hexagon inscribed in a circle having an area of 170 square centimeters.

Three circles of radii 110, 140, and 220 are tangent to one another. What is the area of the triangle formed by joining centers of the circles?

A circle with area 254,469 sq. cm. is circumscribed about a triangle whose area is 48.23 square cm. If one of the triangle measure 18 cm, determine length of the shorter leg of the triangle in cm.

A road is tangent to a circular lake. Along the road and 12 miles from the point of tangency, another road opens toward the lake. From the intersection of the two roads to the periphery of the lake, the length of the new road is 11 miles. If the new road will be prolonged across the lake, find the length of the bridge to be constructed.

The center of two circles with radii of 3 m and 5 m, respectively are 4 m apart. Find the area of the portion of smaller circle outside the larger circle.

Find the area in square centimeter of the largest square that can be cut from a sector of a circle radius 8 cm and central angle 120°.

A circle is inscribed in a square and circumscribed about another. Determine the ratio of the area larger square to the area of the smaller square.

One side of a rectangle, inscribed in a circle of diameter 17 cm, is 8 cm. Find the length of the other side.

The sum of the sides of two polygons is 12 and the sum of their diagonals is 19. The polygons are: