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Geometry

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

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q9. (page 431)

Find the area of each figure:

Short Answer

Expert verified

The area of given figure is 30 square units.

Step by step solution

01

Step 1. Given information.

The sides of triangle are $5, 12$ and 13 .

i.e. $a = 5, b = 12$ and

02

Step 2. Concept used.

Area of triangle can be found using the Heron’s formula

$A = \sqrt{s (s - a) (s - b) (s - c)}$

Where,

Semi perimeter $s = \frac{1}{2} (a + b + c)$

03

Step 3. Find the semi perimeter.

$s = \frac{1}{2} (a + b + c)$

$= \frac{1}{2} (5 + 12 + 13)$

$= \frac{1}{2} (30)$

$= 15$

04

Step 4. Find the area of given figure.

Calculation: $A = \sqrt{s (s - a) (s - b) (s - c)}$

$= \sqrt{15 (15 - 5) (15 - 12) (15 - 13)}$

$= \sqrt{15 (10) (3) (3)}$

$= \sqrt{100}$

$= 30$ Square units.

Therefore, the area of given figure is 30 square units.

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Most popular questions from this chapter

Find the areas of $△ A B C, △ D B C$ and $△ E B C$ .

A better approximation can be found by using 100 smaller rectangles with base vertices at $0, 0.01, 0.02, 0.03, ........, 1.00$ . Change lines $10, 20, 40$ and 50 as follows: $\begin{array}{l} 10^{} L E T^{} X = 0.01 \\ 20^{} F O R^{} N = 1^{} T O^{} 100 \\ 40^{} L E T^{} A = A + Y * 0.01 \\ 50^{} L E T^{} X = X + 0.01 \end{array}$

RUN the program to approximate the area of the shaded region.

The base of a rectangle is $(x + 5)$ and height $(x)$ . What is the area and perimeter of the rectangle?

Find the area and perimeter of a square with sides $5 c m$ long.

The area of a rhombus is 100. Find the length of the two diagonals if one is twice as long as the other.

See all solutions

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