The diagram shows a square ABCD M is the midpoint of AB N is the midpoint of AD The area of the shaded triangle AMN is 8cm^2 Work out the area of triangle MCN

Question

area of triangle and square shaded section 

Comments

Hi, Do you know what paper name this is?

Answer 1

Join B to D. The triangle BAD has twice the dimensions of the shaded triangle so it has 4 times the area=4×8=32cm². But BD is a diagonal of the square, so the area of the square is 2×32=64cm². The square has side length 8, because 8×8=64. 

The short legs of the triangles BCM and CDN have length 4cm and long leg 8cm. So together they have an area of 4×8=32cm². Combined with the area of the shaded triangle their total area is 32+8=40cm², so the area of MCN is 64-40=24cm².

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