Triangle DEF is similar to triangle ABC. AB = 2cm and the area is 5 sq cm...if DE = 6cm, what is the area of DEF?
2007-10-29 12:35:42 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Since they're similar, make a proportion:
2cm/6cm =5sqcm/ (X) area of DEF, then cross-multiply so:
2X=6*5
2X=30
X=15 sq cm=Area of DEF
Answer: 15 sq cm
2007-10-29 12:45:36 · answer #1 · answered by Trew_Q 2 · 0⤊ 1⤋
If the dimension of a side is tripled 2cm --> 6cm, the area is multiplied by the square of this (3²). So the area is 9 times as big.
5 sq. cm. x 9 = 45 sq. cm.
The following diagram mirrors your situation. The triangle ABC has a side AB = 2cm. Similar triangle DEF has a side DE = 6 cm. Notice how you can fit 9 copies of triangle ABC inside of DEF.
Another way to prove this is to use the formula for the area of a triangle. Take AB to be the base, and define h to be the height of the smaller triangle. Since they are similar triangles, DEF will have a height of 3h.
Area triangle ABC = 1/2(2)h = h = 5
Given that the height of triangle ABC is 5, the height of triangle DEF is 15.
Area triangle DEF = 1/2(6)(15) = 1/2(90) = 45
The answer is 45 sq. cm.
2007-10-29 19:39:52 · answer #2 · answered by Puzzling 7 · 0⤊ 1⤋
The area of a triangle = 1/2 x The base x The height.
2007-10-29 19:40:42 · answer #3 · answered by crazy3rboy 4 · 1⤊ 1⤋
Since a triangle is half of a parallelogram and the area of a parallelogram is height times base, then the area of the triangle is 1/2 x base x height
2007-10-29 19:51:03 · answer #4 · answered by Karin H 3 · 0⤊ 1⤋
A=(1/2)bh
Let b = base of triangle
Let h = height of triangle
2007-10-29 19:39:41 · answer #5 · answered by Markynaz 3 · 0⤊ 1⤋
Ok, so you are going to set up a proportion. 2/6= 5 squared/x squared, where x= area of triangle DEF
Then you have to solve the proportion for x, which will be the area of DEF. You should get like 2x squared =150, so x squared= 75, so area of triangle DEF is squrt of 75, or 3 squrt of 5.
2007-10-29 19:41:44 · answer #6 · answered by Anonymous · 0⤊ 3⤋
A = 0.5*base*height
Find the height of ABC, then times it by 3 to get the height of DEF, and then find the area of DEF.
2007-10-29 19:38:12 · answer #7 · answered by I can't think of a good name 2 · 0⤊ 2⤋
ABC = 5sq cm
DEF = 5sq cm * k
Comparing AB and DE:
ab * 1/2base = area_ABC
ABC = 5sq cm = 2 * base/2
base(ABC) = 5sq
=> base(DEF) = 5 * 5/2 = 25/2 = 12.5
Area_DEF = 1/2B * H
= 5cm *1/2(12.5cm)
= 31.25 sq cm or 31 1/4 sq cm
2007-10-29 19:45:01 · answer #8 · answered by David F 5 · 0⤊ 1⤋
to find the area of a triangle the formula is:
A=bxh/2
A=area
b=base
x=multiply
h=height
/=divide
2007-10-29 19:47:39 · answer #9 · answered by Time 2 · 0⤊ 1⤋
equal lateral triangle, isocele triangle, or right angle triangle??
2007-10-29 19:41:05 · answer #10 · answered by Anonymous · 0⤊ 4⤋