MODULE VI LET’S GO MEASURE A KITE!

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Presentation transcript:

MODULE VI LET’S GO MEASURE A KITE!

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.

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.

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.

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?

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).

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

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

AREAS OF QUADRILATERALS 4 cm 5 cm 4 cm 3 cm 10 cm 4 cm 3 cm

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.

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…

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

AREAS OF QUADRILATERALS The method is the same for a kite.

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

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

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