Perimeter and Area | IT

Question 11

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

  1. Find the area of red triangle ABE\text{ABE}.
Question diagram 1
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Solution
Understand the Question
  • The area of a triangle on a grid is calculated using the formula: Area=12×base×height\text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height}
  • Determine the length of the base AB\text{AB} by counting the grid units along the bottom edge.
  • Determine the vertical height by counting the perpendicular grid units from the base AB\text{AB} up to the opposite vertex E\text{E}.

2. Find the area of red triangle ABE\text{ABE}.

Step 1 · Find the Base Length

Count the grid squares along the base segment AB\text{AB}.Diagram 1

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

Step 2 · Find the Perpendicular Height

Count the perpendicular grid units from base AB\text{AB} upwards to vertex E\text{E}.Diagram 2

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

Step 3 · Calculate the Area of Triangle ABE\text{ABE}

Using the area formula for a triangle:

Area of triangle ABE=12×base×height=12×4 units×4 units=12×16 square units=8 square units\begin{aligned} \text{Area of triangle ABE} &= \dfrac{1}{2} \times \text{base} \times \text{height} \\[0.6em] &= \dfrac{1}{2} \times 4 \text{ units} \times 4 \text{ units} \\[0.6em] &= \dfrac{1}{2} \times 16 \text{ square units} \\[0.6em] &= 8 \text{ square units} \end{aligned}
Answer

2. 8 square units8 \text{ square units}

Common Mistakes
  • Forgetting the Factor of 12\dfrac{1}{2}: Multiplying base×height=4×4=16\text{base} \times \text{height} = 4 \times 4 = 16 gives the area of a rectangle rather than a triangle.
  • Using Slanted Side Instead of Height: Measuring along the slanted edges AE\text{AE} or BE\text{BE} instead of measuring the straight perpendicular distance from vertex E\text{E} down to base AB\text{AB}.

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Q9

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Q10

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

  1. 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—

  1. Find the area of red triangle ABE\text{ABE}.
Q12

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Q13

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Q14

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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.

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Q18

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