Area of the Side of a Goal

I noticed that the side of the soccer goal was almost a trapezoid and I decided to use it to find area.

To find the area of the side I extended the lines to make a trapezoid than subtracted the area of the small triangle.

 

Using GSP measurements the area of the shape made by the side of the goal is 45.2395cm^2.
(NW5)

Circumference, Area, and Pie

After taking a picture of this fruit pie (because everyone takes a picture of their food before they eat it these days) I noticed that this pie was a perfect example of a circle, and using some simple formulas, I could find its circumference and area.

After measuring a radii of the circle, I was able to calculate the area and circumference using the formulas shown above. 

But, why stop there? It also became apparent that I could inscribe a polygon inside the circle, and calculate the area of that as well. In this case, I used a trapezoid.

As shown above, I was able to calculate the area of this trapezoid using Theorem 11-5.

It's seems that everything, even a fruit pie, has some relation to math, and more specifically: geometry. 

-RO5

Stylish Geometry

I went to the Gilroy Outlets last weekend and visited the Coach store.  I was looking at the purses when I realized that some of the purses were perfect isosceles trapezoids.  I used Geometer's Sketchpad to prove Theorem 5-18 and Theorem 5-19.

Theorem 5-18 states that the base angles of an isosceles trapezoid are congruent and my picture shows that the base angles are both 69.89 degrees. In Theorem 5-19, the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.  Since segment AD and segment BC were already parallel, then segment EF was parallel as well.  I then measured and added segments AD and BC and concluded that the average was 8.71, which is the same as EF.  Therefore, I  proved that this Coach purse is an isosceles trapezoid and a fashionable accessory!  (~MG1)

Trapezoids in Candy

This candy piece demonstrates the definition of a trapezoid (specifically an isosceles trapezoid), and Theorem 5-18, which states that the base angles of an isosceles trapezoid are congruent.

Lines AB and DC are parallel while AD and BC are not, which fits the qualification: "A quadrilateral with exactly one pair of parallel sides is called trapezoid." It also fits the qualification of an isosceles trapezoid by having congruent legs. Finally, the candy also fulfills Theorem 5-18, because, as you can see, its base angles are congruent. -IR1