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Questions > Grade 20 Geometry > Quadrilaterals -Areas of Triangles

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Question: What is height of triangle DCB, if the area of triangle ADC is half the area of triangle DCB?

A ) H = 2h
B ) H = 4h
C ) H = h2
D ) h² = H

Steps to derive

1 Given, the area of triangle ADC = half of the area of triangle DCB

2 From the figure, triangle ADC and triangle DCB have same base DC, height of triangle ADC is h and the height of triangle BCD is H.

3 Area of a triangle = 12 × base × height
[Formula.]

4 Area of triangle ADC = 12 × area of triangle DCB

[Substitute the values.]
5 12 × DC × h = 12 (12× DC × H)

6 12 × DC × h = 12× 12 × DC × H

[Simplify.]
7 h = H2

[Multiply each side by 2 and simplify.]
8 2h = H

9 Height of triangle DCB = H = 2h

Hence the right answer is Option A

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