Chapter 1: Q10. (page 52)

If the area of $Δ ABD$ is 280, state the area of the polygon $ABCD$ .
A. $560$ B. $630$
C. $700$ D. $840$

Short Answer

Expert verified

Area of the polygon $A B C D$ is $630$ and the correct option isB.

Step by step solution

- Consider the diagram.

From the diagram,

$∠ A = 90 °$ and $∠ D = 90 °$ .

$A B = 16$ , $C D = 20$ .

- Prove that ABCD is a trapezium.

From the diagram,

$∠ A + ∠ D = 180 °$ .

So, sum of interior angles on same side of transversal is $180^{°}$

So, $A B ∥ C D$ .

Thus, $A B C D$ is a trapezium.

- Calculate the area of ABCD.

Given,

Area of $Δ A B D$ is 280.

Again area of triangle is given by:

$Area = \frac{1}{2} \times base \times height$

Area of triangle $A B D$ is:

$\begin{matrix} Area = \frac{1}{2} \times base \times height \\ 280 = \frac{1}{2} \times 16 \times height \\ 280 \times 2 = \frac{1}{2} \times 16 \times height \times 2 \\ \frac{560}{16} = \frac{16}{16} \times height \\ height = 35 \end{matrix}$

Since, $A B C D$ is a trapezium.

Area of $A B C D$ is:

$Area = \frac{(Sum of paralle sides)}{2} \times height$

In $A B C D$ , $A B$ and $C D$ are parallel sides.

And $A B = 16$ , $C D = 20$ and height is 35.

Then area is:

$\begin{matrix} Area = \frac{A B + C D}{2} \times height \\ = \frac{16 + 20}{2} \times 35 \\ = \frac{36}{2} \times 35 \\ = 630 \end{matrix}$

- State the conclusion.

Area of $A B C D$ is 630. Therefore, option B is correct.

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If the area of $Δ ABD$ is 280, state the area of the polygon $ABCD$ .
A. $560$ B. $630$
C. $700$ D. $840$

Short Answer

Step by step solution

- Consider the diagram.

- Prove that ABCD is a trapezium.

- Calculate the area of ABCD.

- State the conclusion.

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If the area of ΔABDis 280, state the area of the polygon ABCD.A. 560 B. 630C. 700 D. 840

Short Answer

Step by step solution

- Consider the diagram.

- Prove that ABCD is a trapezium.

- Calculate the area of ABCD.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Statistics

Geometry

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

If the area of $Δ ABD$ is 280, state the area of the polygon $ABCD$ .
A. $560$ B. $630$
C. $700$ D. $840$