Rectangle and Triangle Area - SSAT Middle Level Quantitative

1. What is the area of a triangle with $b = 7$ and $h = 3.5$?

   $12.25$. Apply the triangle area formula with decimals: $\frac{1}{2} \times 7 \times 3.5 = 12.25$.

2. Identify the missing dimension: A rectangle has area $48$ and width $6$. What is $l$?

   $8$. Divide the area by the width to solve for length: $48 \div 6 = 8$.

3. What is the area of a triangle with $b = 9$ and $h = 8$?

   $36$. Apply the triangle area formula: $\frac{1}{2} \times 9 \times 8 = 36$.

4. Find the area: A rectangle has $l = 11$ and $w = 11$.

   $121$. Multiply the length by the width to find the area: $11 \times 11 = 121$.

5. What is the area of a rectangle with $l = 3.5$ and $w = 6$?

   $21$. Multiply the length by the width, handling decimals: $3.5 \times 6 = 21$.

6. What is the area of a triangle with $b = 12$ and $h = \frac{1}{2}$?

   $3$. Apply the triangle area formula with fractions: $\frac{1}{2} \times 12 \times \frac{1}{2} = 3$.

7. What is the area of a triangle with $b = 16$ and $h = 9$?

   $72$. Apply the triangle area formula: $\frac{1}{2} \times 16 \times 9 = 72$.

8. Identify the missing base: A triangle has area $30$ and height $10$. What is $b$?

   $6$. Solve for base by rearranging the formula: $b = \frac{2 \times 30}{10} = 6$.

9. What is the area of a rectangle with $l = \frac{1}{2}$ and $w = 10$?

   $5$. Multiply the length by the width, including fractions: $\frac{1}{2} \times 10 = 5$.

10. What is the area of a rectangle with $l = 15$ and $w = 2$?

    $30$. Multiply the length by the width to find the area: $15 \times 2 = 30$.

11. What is the area of a triangle with $b = 10$ and $h = 6$?

    $30$. Apply the triangle area formula: $\frac{1}{2} \times 10 \times 6 = 30$.

12. State the formula for the area of a rectangle with length $l$ and width $w$.

    $A = lw$. The area of a rectangle is calculated as the product of its length and width.

13. Find the area: A triangle has $b = 18$ and $h = 4$.

    $36$. Apply the triangle area formula: $\frac{1}{2} \times 18 \times 4 = 36$.

14. What is the area of a rectangle with $l = 9$ and $w = 4$?

    $36$. Multiply the length by the width to find the area: $9 \times 4 = 36$.

15. Identify the missing dimension: A rectangle has area $63$ and length $9$. What is $w$?

    $7$. Divide the area by the length to solve for width: $63 \div 9 = 7$.

16. Find and correct the error: A student writes triangle area as $A = bh$. What is the correct formula?

    $A = \frac{1}{2}bh$. The student omitted the factor of $\frac{1}{2}$, which accounts for the triangular shape being half of a rectangle with the same base and height.

17. Identify the missing width: A rectangle has area $90$ and length $15$. What is $w$?

    $6$. Divide the area by the length to solve for width: $90 \div 15 = 6$.

18. What is the area of a rectangle with $l = 12$ and $w = 5$?

    $60$. Multiply the length by the width to find the area: $12 \times 5 = 60$.

19. What is the area of a triangle with $b = 14$ and $h = 5$?

    $35$. Apply the triangle area formula: $\frac{1}{2} \times 14 \times 5 = 35$.

20. What is the area of a right triangle with legs $5$ and $12$ (use legs as $b$ and $h$)?

    $30$. For a right triangle, use the legs as base and height: $\frac{1}{2} \times 5 \times 12 = 30$.

21. Identify the missing height: A triangle has area $45$ and base $9$. What is $h$?

    $10$. Solve for height by rearranging the formula: $h = \frac{2 \times 45}{9} = 10$.

22. What is the area of a rectangle with $l = 7$ and $w = 8$?

    $56$. Multiply the length by the width to find the area: $7 \times 8 = 56$.

23. Which measurement is used as the height in $A = \frac{1}{2}bh$: the perpendicular distance to the base or any side length?

    The perpendicular distance to the base. The height in the triangle area formula must be the perpendicular distance from the base to the opposite vertex.

24. State the formula for the area of a triangle with base $b$ and height $h$.

    $A = \frac{1}{2}bh$. The area of a triangle is half the product of its base and height.

25. Identify the missing height: A triangle has area $24$ and base $8$. What is $h$?

    $6$. Solve for height by rearranging the formula: $h = \frac{2 \times 24}{8} = 6$.

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