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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: Q34. (page 427)

The diagonals of a rectangle are18cmlong and intersect at a" width="9" height="19" role="math">60∘angle. Find the area of the triangle.

Short Answer

Expert verified

The area of the triangle is $81 \sqrt{3} c m^{2}$ .

Step by step solution

01

Step 1. Given information.

The diagonal of a rectangle are18cm long and intersect at $60^{\circ}$ angle.

02

Step 2. Concept Used.

The area of the rectangle is
$A = l e n g t h \times b r e a d t h$

03

Step 3. Let’s calculate the area of each square and the value of s.

The diagonal of a rectangle are18cm long.

i.e $A C = B D = 18 c m$

We know that the diagonals of a rectangle bisect each other.

Thus $\begin{array}{l} A = l b \\ A = (9 \sqrt{3}) (9) \\ A = 81 \sqrt{3} c m^{2} \end{array}$

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Most popular questions from this chapter

Find the area of each figure:

A rhombus with a $120^{\circ}$ angle and sides 6cm

Find the area of a square with diagonals of lengthd

a. Use the diagram at the right. Find the area of $▱ P Q R S$ .

b. Use the diagram at the right. Find the area of $△ P S R$ .

c. Use the diagram at the right. Find the area of $△ O S R$ . (Hint: Refer to $△ P S R$ and use Exercise28).

d. Use the diagram at the right. What is the area of $△ P S O$ ?

e. Use the diagram at the right. What must the area of $△ P O Q$ be? Why? What must the area of $△ O Q R$ be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

Find the area of each figure:

An isosceles triangle with base10and Perimeter 36 .

An isosceles triangle has sides that are $5 c m, 5 c m$ and8cmlong. Find its area and the lengths of the three altitudes.

See all solutions

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