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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 11: Q28. (page 432)

$\overset{炉}{A M}$ is a median of $鈻� A B C$
Prove: Area of $鈻� A M B = \frac{1}{2}$ Area of $鈻� A B C$

Short Answer

Expert verified

Hence proved

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

Step by step solution

01

Step 1. Modify the given diagram.

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

02

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 $鈻� A B C$

Then,

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

03

Step 3. Use the concept of area of triangle.

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

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

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

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

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

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Most popular questions from this chapter

Use a calculator or the trigonometry table on page 311to find the area of each figure to the nearest tenth.

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The base of a rectangle is 16cmand perimeter is42cm. What is the area and height of the rectangle?

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