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The Area of trapezoids, rhombi, and kites exercise appears under the 6th grade (U.S.) Math Mission, High school geometry Math Mission and Mathematics I Math Mission. This exercise practices finding the area of various quadrilaterals.

Types of Problems

There are three types of problems in this exercise:

  1. Find the area of the trapezoid: This problem provides a picture of a trapezoid. The user is asked to correctly find the area of the trapezoid and write the answer in the space provided.
    Aotrak1

    Find the area of the trapezoid

  2. Find the area of the parallelogram: This problem provides a picture of a parallelogram. The user is asked to correctly find the area of the parallelogram and write the answer in the space provided.
    Aotrak2

    Find the area of the parallelogram

  3. Find the area of the kite/rhombus: This problem provides a picture of a kite or rhombus. The user is asked to correctly find the area of the kite or rhombus and write the answer in the space provided.
    Aotrak3

    Find the area of the kite/rhombus


Strategies

Knowledge of the area formulas for quadrilaterals is necessary before beginning on this exercise. Knowing the different properties among quadrilaterals based on the quadrilateral hierarchy can also help.

  1. The formula for the area of a trapezoid is half the product of the height and the sum of the bases, i.e., {A = \frac{1}{2}\times (b_1+b_2)\times h}.
  2. The formula for the area of a parallelogram is base times height
  3. The formula for the area of a rhombus or a kite is half the product of the diagonals ({A = \frac{pq}{2}}).
  4. A rhombus is a special type of a kite.
  5. The title of the exercise does not indicate that general parallelograms will show up, but they do, so be prepared. The area of a parallelogram is the base multiplied by the height ({A = b\times h})

Real-life Applications

  1. Architects use lots of geometry when building bridges, roofs on houses, and other structures.
  2. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.

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