Area Concepts (Triangles with Common Bases or Heights)

Given: Common Base, Combined Height
Find: Combined Area

First
The figure below, not drawn to scale, shows two shaded triangles in a rectangle of length 20 cm and breadth 16 cm. What fraction of the whole figure is shaded?

(Express your answer in the simplest form.)

 

Method 1: Find Areas

Shaded Area
= Combined Area of 2 Triangles
= 1/2 × Common Base x Combined Height
= 1/2 × 12 cm × 16 cm
= 96 cm^2

Area of Rectangle
= length x breadth
= 20 cm x 16 cm
= 320 cm^2

Fraction (Shaded Area / Whole Area)
= 96 / 320 = 3 / 10

Method 2: Formulas in Ratios

Combined Height = Breadth

Shaded Area : Whole Area
= 1/2 × Common Base × Combined Height : Length x Breadth
= 1/2 × Common Base : Length
= 1/2 × 12 : 20
= 3 : 10
= 3 / 10