## Measurement

### High School Level Questions on Area and Surface Area from the Dr. Math Archives

High School Dr. Math Questions on Measurement

Below are some questions and answers from our archive of questions sent via e-mail by K12 students and teachers to Ask Dr. Math. You may also browse the entire high school level archive by category.

### Area and Surface Area

#### Area and Perimeter

Area and Perimeter: Mowing the Lawn
How many circuits are necessary to cut half the lawn?
If You Know Perimeter, Can You Find Area?
Can one determine the acreage of an irregularly shaped field if only the distance around the edge of the field (in feet) is known?
Isoperimetric Inequalities
How can I prove that a circle has more area inside given its border length than any other shape?

#### Area of Polygons

Area of a Hexagon
How do you calculate the area of a hexagon?
Area of a Hexagon - Calculation
I've been trying to find a simple way to calculate the area of a hexagon given only it's width between two parallel sides.
Area of an Irregular Polygon Given Side Length
What is the area of an irregular quadrilateral with side lengths in a clockwise order of 43.61, 133.64, 146.96, and 110.85?
Area of a Rectangle Outside a Rectangle
Find the area of the concrete border of a rectangular swimming pool.
Area of a Square Inscribed in a Circle
What is the area of a square inscribed in a circle whose circumference is 16 (pi).
Area of a Triangle
Knowing one side measures 1 and two adjacent angles measure a and b...
Area of Triangles using Hero's Formula
If a person gave three dimensions of a triangle (in feet) and noted the base dimension, without knowing the angles because the other two lines would have to intersect someplace, is there a formula that could calculate the area?
Area of an unspecified triangle
A square ABCD, with side "y", and an equilateral triangle DEF, with the same side "y", are in contact at point "d"...
Finding Polygon Areas
How do I find the area of polygons?
I need to find the area of a 4-sided figure, given its side lengths.

#### Surface Area

Bell Tower Painting
I need to know the total surface area of three domes with assorted radii.
Cone Surface Area
What is the area of a cone when given the height and the angle at the convergence point?
Cylinder Surface Area
What is the formula to calculate the surface of a cylinder with 25cm diameter and 20cm height?
Cylinder Surface
What is the general formula for the surface of a Cylinder?
Pentagonal Pyramid Area
I would like to know the area of a pentagonal pyramid. The dimensions of the sides of the base are 5cm ea. and the height is 23cm.
Rectangular Prism
Is it possible to have a rectangular prism that has a volume greater than its surface area?
Right Circular Cone - Surface Area
Could you please tell me the formula for finding the surface area of a right circular cone?
Sphere: Surface Area of Earth
Could you tell me the formula for determining the surface area of a sphere?

#### Area and Circles

Area, Angle of Chords of a Circle
Calculate the angles PAB and POB, the area of the sector bounded by OP, OB and the minor arc PB.
Circle Inscribed in Triangle
What is the radius of a circle inscribed in a 3-4-5 right triangle?
Cow Grazing in Circles
A cow is tied to a 100 ft. rope (stay with me -- this _is_ interesting). His rope is tied to a pole in the center of a circle of radius 50 ft. This circle has a ten foot opening, out of which the cow can walk and graze. What's the area of grazing?
Goat tied to a barn
If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? Assume the goat is tied to a corner.
Another Grazing Cow
A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing?

#### Area and Volume

Cone: Area, Volume
What are the formulae to find the volume and area of a cone?
Football: Area and Volume
How would one find the area of a football? Or then again, how would one find the volume of a football?
Pear: Area, Volume
How do you find the area and volume of a pear?
Rectangular Solid: Area
How do you calculate the lateral area, total area, and volume of a rectangular solid with the following dimensions...
Sphere Formulas
What are the formulas for area and volume of a sphere?
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Mara Landers