Perimeter and Area | IT

Question 11

Use your understanding from previous grades to calculate the area of any closed figure using grid paper and—

Find the area of red triangle ABE.

Solution

We can find the area of a triangle using its base and its height.

Step 1 — Find the base length

Let us look at the red triangle ABE. The base of the triangle is the line segment AB. We count the grid squares along the bottom edge. The length of AB is 4 units.

$\text{Base (AB)} = \text{4 units}$

$\boxed{\text{Base} = \text{4 units}}$

Diagram 1

Step 2 — Find the height

The height is the distance from point E to the base AB. This distance must be perpendicular to the base. We count the grid squares upwards from the base AB to point E. The height is 4 units.

$\text{Height} = \text{4 units}$

$\boxed{\text{Height} = \text{4 units}}$

Diagram 2

Step 3 — Calculate the area

The formula for the area of a triangle is half times base times height. We will use the base and height we found.

$\text{Area of triangle ABE} = \frac{1}{2} \times \text{base} \times \text{height}$

$= \frac{1}{2} \times \text{4 units} \times \text{4 units}$

$= \frac{1}{2} \times \text{16 square units}$

$= \text{8 square units}$

$\boxed{\text{Area of triangle ABE} = \text{8 square units}}$

Answer

(ii) The area of red triangle ABE is 8 square units.

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Find out the length of the boundary (i.e., the perimeter) of each of the other arrangements below.

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Q10

Use your understanding from previous grades to calculate the area of any closed figure using grid paper and—

Find the area of blue triangle BAD.

Q11

Use your understanding from previous grades to calculate the area of any closed figure using grid paper and—

Find the area of red triangle ABE.

Q12

Area of rectangle ABCD = ________

Q13

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What is the largest perimeter possible?
Make a figure with a perimeter of 18 units.
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Q14

Let's do something tricky now! We have a figure below having perimeter 24 units.

Without calculating all over again, observe, think and find out what will be the change in the perimeter if a new square is attached as shown on the right.

Q15

Experiment placing this new square at different places and think what the change in perimeter will be. Can you place the square so that the perimeter: a) increases; b) decreases; c) stays the same?

Q16

Below is the house plan of Charan. It is in a rectangular plot. Look at the plan. What do you notice?

Some of the measurements are given.

a. Find the missing measurements.

b. Find out the area of his house.

Q17

Now, find out the missing dimensions and area of Sharan's home. Below is the plan:

Some of the measurements are given.

a. Find the missing measurements.

b. Find out the area of his house.

What are the dimensions of all the different rooms in Sharan's house? Compare the areas and perimeters of Sharan's house and Charan's house.

Q18

Area Maze Puzzles

In each figure, find the missing value of either the length of a side or the area of a region.