Question

100 Points! Please help with this geometry question! Give an explanation, it could be short or statement reasonings! Thanks!

Answer 1

• 168 cm²

Explanation:

Refer to attached

Given

• Area of ΔDCF = 63 cm²

To find

• Area of ΔABC

Solution

• Let the area of ABC be A, then
• A = 1/2bh, where b= AC is the base and h is the height of the triangle

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The triangle DCF can be divided into DEC and DEF as per picture and the area of them is:

Area of ΔDEF

• 1/2DE*h2

Area of ΔDEC

• 1/2DE*h1

Since D and E are midpoints of AB and BC:

• DE = 1/2AC = 1/2b

• And h1 = 1/2h,
• h2 = 1/2h1 = 1/2*1/2h = 1/4h

So the area of ΔDCF is:

• 1/2(1/2bh1) + 1/2(1/2bh2) =
• 1/2(1/2b*1/2h) + 1/2(1/2b*1/4h) =
• 1/8bh + 1/16bh =
• 3/16bh

Since the area of ABC is A = 1/2bh we have:

• 3/8*1/2bh = 3/8A and
• 3/8A = 63

Solving for A:

• A = 63*8/3 = 168 cm²