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**MODULE VI LET’S GO MEASURE A KITE!**

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**AREAS OF QUADRILATERALS**

We have already discussed how to find the area of certain parallelograms. Today, we are going to extend that knowledge and learn how to find some new areas.

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**AREAS OF QUADRILATERALS**

Again, to find the areas of figures, we must recall their parts. The first figure, we will discuss today is a trapezoid.

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**AREAS OF QUADRILATERALS**

Remember: A trapezoid is a figure with exactly one pair of opposite parallel sides. Recall also that the two parallel sides of a trapezoid are called its bases.

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**AREAS OF QUADRILATERALS**

The height of a trapezoid is the perpendicular distance between its bases. Now keep in mind, since the other pair of sides cannot be parallel, the bases of a trapezoid CANNOT be equal. So how do we find the area?

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**AREAS OF QUADRILATERALS**

In order to find the area of the trapezoid we must find the average of the two bases, then multiply by the height. In short, ½ h(b1 + b2).

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**AREAS OF QUADRILATERALS**

And that makes sense…because if I piece two congruent trapezoids together it’s just a parallelogram. And the original trapezoid will make up half the area of that parallelogram. b1 b2 h b2 b1

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**AREAS OF QUADRILATERALS**

Like with parallelograms, we can use our knowledge of triangles to discover things about trapezoids. If the figure below is an isosceles trapezoid, then what is its area? 4 cm 5 cm 10 cm

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**AREAS OF QUADRILATERALS**

4 cm 5 cm 4 cm 3 cm 10 cm 4 cm 3 cm

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**AREAS OF QUADRILATERALS**

So, since the height was 4 cm and the average of the bases was 7 cm, the area of the trapezoid is 28 cm2.

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**AREAS OF QUADRILATERALS**

Finding the area of a rhombus or a kite is even easier! Now, since a rhombus is a parallelogram, we can use our old method of base times height. Or we can use this new method…

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**AREAS OF QUADRILATERALS**

The area of both a rhombus and a kite is represented by A = ½ d1d2 d represent diagonals. d1 d2

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**AREAS OF QUADRILATERALS**

The method is the same for a kite.

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**AREAS OF QUADRILATERALS**

It will be important for you to remember the special properties of rhombi and kites. For instance, given that the figure below is a rhombus, find its area… 3 cm 6 cm

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**AREAS OF QUADRILATERALS**

In rhombi, both diagonals bisect each other. In kites, only one diagonal is bisected.

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**AREAS OF QUADRILATERALS**

However, the diagonals of both rhombi and kites, meet at a right angle. Find the perimeter of the rhombus below. 9 cm 12 cm

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Special Parallelograms. Theorem 6-9 Each diagonal of a rhombus bisects the opposite angles it connects.

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