Heron Isn't Needed

Geometry Level 1

The above diagram shows two right triangles 6-8-10 and 8-15-17 joined to form a large triangle with side lengths 10-17-21.

What is the area of this large triangle?


The answer is 84.

Chung Kevin by Chung Kevin , 46, Australia

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1 solution

Relevant wiki: Area of Triangles - Problem Solving - Easy

Area of Triangle = 1 2 × base × height . ⟹ Area = 1 2 × ( 15 + 6 ) × 8. = 84 . \large \displaystyle \text{Area of Triangle } = \frac{1}{2} \times \text{base } \times \text{height }.\\ \large \displaystyle \implies \text{Area} = \frac{1}{2} \times (15+6) \times 8. = \color{#20A900}{\boxed{84}}.

Or \large \color{#D61F06}{\text{Or}}

Total Area = Area of first triangle + Area of second triangle. Total Area = 1 2 × 6 × 8 + 1 2 × 15 × 8. ⟹ Area = 24 + 60 = 84 . \large \displaystyle \text{Total Area = Area of first triangle + Area of second triangle.}\\ \large \displaystyle \text{Total Area } = \frac{1}{2} \times 6 \times 8 + \frac{1}{2} \times 15 \times 8.\\ \large \displaystyle \implies \text{Area} = 24 + 60 = \color{#20A900}{\boxed{84}}.

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That is correct! Of course, we can solve this question by Heron's formula as well (as hinted in the title), but that is unnecessary.

Chung Kevin - 5 years, 1 month ago

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Heron't formula is for scalar triangle.

Since we have a right angled triangle. There is no need of Heron's Formula.

Samara Simha Reddy - 5 years, 1 month ago

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