Question

In the given figure, the area of square ABCD is 4 cm² and E any point on AB. F, G, H and Kare the mid-point of DE, CF, DG, and CH respectively. The area of triangleKDC ?​

Answer 1

Answer:

The area of triangle KDC is 1/8 cm².

Step-by-step explanation:

1. First draw a line from point E to corner C to make a line EC.
2. You know that E is the mid point so AE = BE.
3. As, ABCD is a square, so AD = BC is there.
4. If you have common sense, then you can now easily prove that ED = EC. And if don't have that then you need to do CONGRUENCY OF TRIANGLES in SAS here to get ED = EC (cpctc).
5. If you calculate it or use your topper sense then you will find that Area of EDC = 1/2 × Area of ABCD.

• Area of EDC = 1/2 × Area of ABCD
• => Area of EDC = 1/2 × 4cm²
• => Area of EDC = 2cm²

Then, Area of FDC = 1/2 × Area of EDC because F is the mid point of ED

• Area of FDC = 1/2 × EDC
• => Area of FDC = 1/2 × 2
• => Area of FDC = 1 cm²

Then this process repeats on until you reach triangle KDC.

But to help you, I will give you the measurements. You can just check out.

1. Area of EDC = 2 cm²
2. Area of FDC = 1 cm²
3. Area of GDC = 1/2 cm²
4. Area of HDC = 1/4 cm²
5. Area of KDC = 1/8 cm²

So, the answer of Area of KDC is 1/8 cm².