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directions: Scrutinize each slide carefully, and you will do well. Welcome Rutherford County Students to the Area of triangle lesson and quiz. My name is MizzterG and I hope this lesson helps you! Triangles are three sided polygons. There are many ways to classify them, but that's another lesson. The great thing about finding the area of a triangle is that you really only need to know two things. 3 cm height If you know the base and the height of the triangle, you will be able to find the area. The key is to already know how to find the area of a rectangle. 4 cm base comma Remember that the formula for the area of a rectangle is length times width. A= L x W The area of this rectangle is four times three. You can also multiply three times four since multiplication is commutative. 3 A= L x W 4 3 x 4 = Type in an answer. square units Now that you remember the formula for the area of a rectangle, lets drop that triangle on top . 3 A= L x W 4 There we go. As you can see, the triangle only covers part of the rectangle. As a matter of fact, it only covers half of it! 3 A = L x W 4 That means this formula won't work for a triangle. What's the formula that will work for the area of a triangle you ask. Hmmm? 3 A = L x W 4 3 x 4 = 12 Well, since the triangle only covers half of the rectangle, just take half of the answer for the area of the rectangle and you've got it! 3 4 3 ½ of the length times width Well, since the triangle only covers half of the rectangle, just take half of the answer for the area of the rectangle and you've got it! 4 ½ x 3 x 4 3 Multiply the length times the width and then just divide by two. ½ of the length times width 4 3 x 4 2 = ½ x 3 x 4 square units 3 x 4 2 = 6 square units If you answered this, you got it right! A= We can write the formula for the area of a triangle in a few ways: ½ b x h A= b x h 2 They all mean the same thing. Start like you are getting the area of a rectangle, then divide by two. A= 1 2 bh Obviously, the areas of these two shapes can't be the same. If you look carefully, you see the triangle is half of the rectangle. 4cm 2cm 4cm 2cm The same amount of squares are not shaded. Use the formulas to find the areas. 4cm 2cm 4cm 2cm Area of a rectangle A= L x W Area of a triangle A= ½ x L x W or half L x W 4cm 2cm 4cm 2cm 4cm A= sq. units 2cm 4cm This one is half of the other!!!! A= 2cm sq. units 4cm A= 8 sq. units ANSWERS 2cm 4cm This one is half of the other!!!! A= 2cm 4 sq. units Let's try a demonstration in case you didn't get it. Click on the next few slids to see me chop the rectangle in half. That way, you will see how the formula works. 4mm A= 5mm mm2 Here is a rectangle. A= L x W 4mm A= 20 5mm mm2 Now let's chop it in half. answer HI-SA! 4mm Area of both triangles together 5mm The area of the two triangles together has not changed. mm2 4mm Area of both triangles together 5mm The area of the two triangles together has not changed. 20 mm2 4mm 5mm Area of just this triangle? Remember, half of the base times the height. mm2 4mm 5mm Area of just this triangle? Remember, half of the base times the height. mm2 don't worry about this side. 5mm 4mm 4mm 10 5mm Each half of the rectangle is 10mm2 mm2 Together they are 20 mm2 10 5mm mm2 4mm Area of a triangle = Area of a triangle = b x h b x Area of a triangle = quiz time! 1 2 b x h 10 ft 8 ft ft2 A = ½ b x h 4cm 4cm cm2 8cm 4cm cm2 cm2 3cm 10cm mm 1 A= 20 20 mm mm2 mm A= mm2 2 mm Hmm? This triangle looks a bit different. Don't panic. Just remember the formula. ½ b x h. This triangle has a base of 10 mm. This triangle has a base of 10 mm. One side is 8 mm. The third side is 9 mm. Don't let these two trick you. We must have the height. 8mm 10mm 9mm The height is 7 mm. The height of this triangle is from it's tallest point to the base. You have to measure in the middle. ½ 7x 10= So to find the area of this triangle, you would use ½ b x h or ½ 7 x 10. mm2 8mm 7mm 10mm 9mm ½ 7x 10= Answer 70 Don't let the other sides distract you. You must use the base and the height only. 2 35 mm2 8mm 7mm 10mm 9mm 10mm 5mm 13mm Make sure you pick the base and the height before dividing by 2. 10mm 5mm A = 13mm mm2 10mm 5mm A = 13mm ½ 5x10 50 2 = 25 mm2 answer 12cm 8cm 5cm 11cm use the base and height! A = cm2 distracter 8x5 2 base = 12cm 40 2 height = 8cm 5cm 20 distracter 11cm use the base and height! A = 20 cm2 7cm 9cm 4cm 6cm use the base and height! A = cm2 don't forget to divide by 2 7cm 3cm 20cm 15cm use the base and height! A = cm2 don't forget to divide by 2 See you soon! |