Chapter 2: Q1. (page 106)

1.In the figure, $∠ B and ∠ B C D$ are right angles. $\bar{B C}$ is 9 units, $\bar{A B}$ is 12 units and $\bar{C D}$ is 8 units. What is the area, in square units of $Δ A C D$ ?
$A . 36 B. 60 C.72 D.135$

Short Answer

Expert verified

The area of $Δ A C D$ is 36 square units.

Step by step solution

Step-1 – Apply the concept of area of a triangle

The area of the triangle is given by $A = \frac{1}{2} b h$ , where bis the base and his the height of the triangle.

For example, suppose a triangle has its base as $16 c m$ and 10cm as its height then the area of the triangle is given by

\begin{matrix} Areaoftriangle= \frac{1}{2} b h \\ = \frac{1}{2} (16) (10) \\ = 80 \end{matrix}

Step-2 – Construct a square

Construct a line AMperpendicular to side $D C$ from the point A.

Therefore, the following is obtained:

Since a square is formed, $\bar{A M} = 9 c m$ and $\bar{M C} = 12 c m$ . Therefore,

\begin{matrix} \bar{M D} = \bar{M C} - \bar{D C} \\ = 12 - 8 \\ = 4 \end{matrix}

Step-3 – Find the area of the triangle AMC

In $Δ A M C$ , the base is 12 units and height is 9 units.

Therefore the area is given by

\begin{matrix} Areaof Δ AMC= \frac{1}{2} b h \\ = \frac{1}{2} (12) (9) \\ = 54 squareunits \end{matrix}

Step-4 – Find the area of the triangle AMD

In $Δ A M D$ , the base is 4 units and height is 9 units.

Therefore the area is given by

$\begin{matrix} Areaof Δ AMC= \frac{1}{2} b h \\ = \frac{1}{2} (4) (9) \\ = 18 squareunits \end{matrix}$

Step-5 – Find the area of the triangle ACD

Area of $Δ A C D$ is found using the area of $Δ A M C and Δ A M D$ as follows:

$\begin{matrix} Areaof Δ ACD=Areaof Δ AMC - Areaof Δ AMD \\ = 54 - 18 \\ = 36 squareunits \end{matrix}$

Hence option A is correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

1.In the figure, $∠ B and ∠ B C D$ are right angles. $\bar{B C}$ is 9 units, $\bar{A B}$ is 12 units and $\bar{C D}$ is 8 units. What is the area, in square units of $Δ A C D$ ?
$A . 36 B. 60 C.72 D.135$

Short Answer

Step by step solution

Step-1 – Apply the concept of area of a triangle

Step-2 – Construct a square

Step-3 – Find the area of the triangle AMC

Step-4 – Find the area of the triangle AMD

Step-5 – Find the area of the triangle ACD

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Decision Maths

Calculus

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

1.In the figure, ∠Band∠BCD are right angles. BC¯is 9 units, AB¯is 12 units and CD¯is 8 units. What is the area, in square units of ΔACD?A.36 B. 60 C.72 D.135

Short Answer

Step by step solution

Step-1 – Apply the concept of area of a triangle

Step-2 – Construct a square

Step-3 – Find the area of the triangle AMC

Step-4 – Find the area of the triangle AMD

Step-5 – Find the area of the triangle ACD

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Decision Maths

Calculus

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

1.In the figure, $∠ B and ∠ B C D$ are right angles. $\bar{B C}$ is 9 units, $\bar{A B}$ is 12 units and $\bar{C D}$ is 8 units. What is the area, in square units of $Δ A C D$ ?
$A . 36 B. 60 C.72 D.135$