Chapter 11: Q28. (page 432)

$\bar{A M}$ is a median of $△ A B C$
Prove: Area of $△ A M B = \frac{1}{2}$ Area of $△ A B C$

Short Answer

Expert verified

Hence proved

$Area of △ A M B = \frac{1}{2} Area of △ A B C$

Step by step solution

Step 1. Modify the given diagram.

Given that base $b = 16$ and Height $h = 5$

Step 2. Concept used.

The median of a triangle is a line segment joining the vertex of the triangle to the mid-point of its opposite side. It bisects the opposite side, dividing it into two equal parts.

Since $A M$ is the median of $△ A B C$

Then,

$\begin{array}{l} B M = M C \\ B C = 2 B M \end{array}$

Step 3. Use the concept of area of triangle.

Area of $△ A B C$ can be found using the formula

$\begin{matrix} A = \frac{1}{2} b h \\ = \frac{1}{2} (B C) (h) \\ = \frac{1}{2} (2 B M) (h) \\ = B M \times h ........... (i) \end{matrix}$

Area of $△ A M B$ can be found using the formula

$\begin{array}{l} A = \frac{1}{2} b h \\ A = \frac{1}{2} (B M) (h) \\ A (A M B) = \frac{1}{2} A (A B C) [f r o m (i)] \end{array}$

Therefore, the Area $△ A M B = \frac{1}{2}$ of Area of $△ A B C$

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$\bar{A M}$ is a median of $△ A B C$
Prove: Area of $△ A M B = \frac{1}{2}$ Area of $△ A B C$

Short Answer

Step by step solution

Step 1. Modify the given diagram.

Step 2. Concept used.

Step 3. Use the concept of area of triangle.

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AM¯is a median of△ABCProve: Area of△AMB=12Area of△ABC

Short Answer

Step by step solution

Step 1. Modify the given diagram.

Step 2. Concept used.

Step 3. Use the concept of area of triangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

$\bar{A M}$ is a median of $△ A B C$
Prove: Area of $△ A M B = \frac{1}{2}$ Area of $△ A B C$