Explanation:
We are given a worksheet with 10 shapes. For each, we need to find the missing side(s), area, or perimeter using formulas for rectangles, squares, and right triangles.
Let’s go one by one.
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1. Rectangle
Given: one side = 5 cm, area = 20 cm²
Area of rectangle = length × width
So, 5 × ? = 20 → ? = 20 ÷ 5 =
4 cm
Perimeter = 2×(length + width) = 2×(5 + 4) = 2×9 =
18 cm
But the table only asks for the missing side (the blank under “Sides”), so answer is
4 cm.
Wait — look at the table: column “Sides” has blanks like “5cm, _____”, meaning two sides are listed (for rectangle: length and width). So yes, missing side is 4 cm.
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2. Square
Given: area = 36 mm²
For square: area = side² → side = √36 =
6 mm
So both sides are 6 mm → missing side =
6 mm
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3. Rectangle
Given: one side = 4 cm, perimeter = 20 cm
Perimeter = 2×(l + w) → 20 = 2×(4 + w)
Divide both sides by 2: 10 = 4 + w → w =
6 cm
So missing side =
6 cm
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4. Square
Given: perimeter = 80 cm
Perimeter of square = 4 × side → side = 80 ÷ 4 =
20 cm
So missing side =
20 cm
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5. Right triangle
Given: one leg = 3 m, area = 6 m²
Area of right triangle = (1/2) × leg₁ × leg₂
So: 6 = (1/2) × 3 × x → 6 = 1.5x → x = 6 ÷ 1.5 =
4 m
So missing side =
4 m
(Also, hypotenuse would be √(3² + 4²) = 5 m, but not asked.)
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6. Square
Given: perimeter = 64 cm
Side = 64 ÷ 4 =
16 cm
Missing side =
16 cm
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7. Rectangle
Given: one side = 6 cm, perimeter = 32 cm
Perimeter = 2×(l + w) → 32 = 2×(6 + w) → 16 = 6 + w → w =
10 cm
Missing side =
10 cm
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8. Rectangle
Given: one side = 8 cm, area = 72 cm²
Area = l × w → 72 = 8 × w → w = 72 ÷ 8 =
9 cm
Missing side =
9 cm
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9. Square
Given: area = 64 mm²
Side = √64 =
8 mm
Missing side =
8 mm
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10. Right triangle
Given: one leg = 6 m, area = 24 m²
Area = (1/2) × leg₁ × leg₂
24 = (1/2) × 6 × x → 24 = 3x → x =
8 m
Missing side =
8 m
Now let’s collect all missing values in order:
1. 4 cm
2. 6 mm
3. 6 cm
4. 20 cm
5. 4 m
6. 16 cm
7. 10 cm
8. 9 cm
9. 8 mm
10. 8 m
Double-check each:
1. 5 × 4 = 20 ✔️
2. 6² = 36 ✔️
3. 2×(4+6)=20 ✔️
4. 4×20=80 ✔️
5. ½×3×4 = 6 ✔️
6. 4×16=64 ✔️
7. 2×(6+10)=32 ✔️
8. 8×9=72 ✔️
9. 8²=64 ✔️
10. ½×6×8 = 24 ✔️
All correct.
Final Answer:
1. 4 cm
2. 6 mm
3. 6 cm
4. 20 cm
5. 4 m
6. 16 cm
7. 10 cm
8. 9 cm
9. 8 mm
10. 8 m
Parent Tip: Review the logic above to help your child master the concept of perimeter and area worksheet 6th grade.
