Triangle Area - ISEE Lower Level Mathematics Achievement

1. What is the area of a triangle with base $b=4$ and height $h=11$?

   $22$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

2. What happens to the area if both base and height are tripled?

   Area becomes $9$ times as large. Area scales with the product of base and height, so tripling both multiplies area by $3\times^3=9$.

3. Identify the missing value: $A=24$ and $b=8$. What is the height $h$?

   $6$. Rearrange $A=\frac{1}{2}bh$ to solve for height by multiplying area by 2 and dividing by base.

4. What happens to the area if the base stays the same and the height is doubled?

   Area doubles. Since area is directly proportional to height when base is fixed, doubling height doubles the area.

5. Identify the missing value: $A=45$ and $h=9$. What is the base $b$?

   $10$. Rearrange $A=\frac{1}{2}bh$ to solve for base by multiplying area by 2 and dividing by height.

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

   $30$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

7. What is the area of a triangle with base $b=12$ and height $h=5$?

   $30$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

8. What is the area of a triangle with base $b=14$ and height $h=14$?

   $98$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

9. Find and correct the formula error: $A=bh$ for a triangle with base $b$ and height $h$.

   Correct: $A=\frac{1}{2}bh$. The given formula omits the factor of $\frac{1}{2}$, which accounts for the triangular shape.

10. Identify the missing value: $A=27$ and $h=6$. What is the base $b$?

    $9$. Rearrange $A=\frac{1}{2}bh$ to solve for base by multiplying area by 2 and dividing by height.

11. What is the area of a triangle with base $b=20$ and height $h=12$?

    $120$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

12. What is the area of a triangle with base $b=7$ and height $h=4$?

    $14$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

13. Which expression correctly gives the height $h$ in terms of area $A$ and base $b$?

    $h=\frac{2A}{b}$. Solving the area formula for height yields this expression by isolating $h$.

14. What is the area of a triangle with base $b=25$ and height $h=8$?

    $100$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

15. Identify the missing value: $A=63$ and $b=14$. What is the height $h$?

    $9$. Rearrange $A=\frac{1}{2}bh$ to solve for height by multiplying area by 2 and dividing by base.

16. State the formula for the area of a triangle using base $b$ and height $h$.

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

17. What is the area of a triangle with base $b=15$ and height $h=2$?

    $15$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

18. Which expression correctly gives the base $b$ in terms of area $A$ and height $h$?

    $b=\frac{2A}{h}$. Solving the area formula for base yields this expression by isolating $b$.

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

    $36$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

20. What is the area of a triangle with base $b=18$ and height $h=3$?

    $27$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

21. What is the area of a right triangle with legs $6$ and $8$ (use them as $b$ and $h$)?

    $24$. For a right triangle, the legs serve as base and height in the area formula $A=\frac{1}{2}bh$.

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

    $72$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

23. Identify the missing value: $A=56$ and $b=16$. What is the height $h$?

    $7$. Rearrange $A=\frac{1}{2}bh$ to solve for height by multiplying area by 2 and dividing by base.

24. What is the area of a triangle with base $b=13$ and height $h=10$?

    $65$. Apply the formula $A=\frac{1}{2}bh$ by multiplying base and height, then dividing by 2.

25. Identify the missing value: $A=30$ and $h=5$. What is the base $b$?

    $12$. Rearrange $A=\frac{1}{2}bh$ to solve for base by multiplying area by 2 and dividing by height.

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