Heron's Formula: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Which set of proposed lengths can form a nondegenerate triangle?

Answer choices for question 1 A 8, 15, and 23 units B 8, 15, and 24 units C 8, 15, and 20 units D 0, 15, and 15 units
2

The sides of a triangle measure 5.4 m, 7.6 m, and 9.8 m. What is its semiperimeter?

Answer choices for question 2 A $11.4$ m B $11.3$ m C $13$ m D $22.8$ m
3

Two rods measure 14 cm and 18 cm. A third rod measures 32 cm. What happens when you try to make a triangle?

Answer choices for question 3 A They form a nondegenerate triangle. B The shorter rods leave a gap even when stretched along the longest. C The two shorter lengths must be equal for the rods to form a triangle. D The rods can only meet in a flat arrangement.
4

Three positive lengths $a$ , $b$ , and $c$ pass the strict triangle inequality. What does the factor $s-b$ measure?

Answer choices for question 4 A The full perimeter minus side length $b$ . B The semiperimeter minus side length $b$ . C The sum of side lengths $a$ and $c$ . D Half of side length $b$ .
5

A triangle has side lengths 12, 17, and 23 units. Which product belongs under the square root in Heron's formula?

Answer choices for question 5 A $26\cdot12\cdot17\cdot23$ B $52\cdot40\cdot35\cdot29$ C $26\cdot14\cdot9\cdot3$ D $14\cdot9\cdot3$
6

Why is the factor $s-c$ positive in a nondegenerate triangle?

Answer choices for question 6 A The full perimeter is greater than $c$ . B The sum of the other two sides is greater than $c$ . C The side $c$ is always the shortest. D The formula replaces negative factors with their absolute values.
7

The triangle shown has sides 15 cm, 15 cm, and 18 cm. What is its exact area?

Answer choices for question 7 A $108$ $\text{cm}^2$ B $216$ $\text{cm}^2$ C $135$ $\text{cm}^2$ D $11664$ $\text{cm}^2$
8

An exact area is $7\sqrt{13}$ square centimeters. Which report gives it to the nearest tenth of a square centimeter?

Answer choices for question 8 A $K=25.2\text{ cm}^2$ B $K\approx25.3\text{ cm}^2$ C $K\approx25\text{ cm}^2$ D $K\approx25.2\text{ cm}^2$
9

A panel has side lengths 9 cm, 10 cm, and 13 cm. Its semiperimeter is 16 cm. What is the exact area?

Answer choices for question 9 A $12\sqrt{14}\text{ cm}$ B $12\sqrt{14}\text{ cm}^2$ C $24\sqrt{7}\text{ cm}^2$ D $2016\text{ cm}^2$
10

Three pieces are recorded as 12 m, 950 cm, and 14 m. What should you do before checking the strict triangle inequality or applying Heron's formula?

Answer choices for question 10 A Square the three measurements. B Round all three lengths to the nearest ten. C Use the numbers 12, 950, and 14 directly. D Convert the three lengths to a common unit.
11

A triangle has area 102 square units. What is the perpendicular height to its 17-unit side?

Answer choices for question 11 A 6 units B 17 units C 12 units D 24 units
12

What algebraic identity turns a squared difference of the form $X^2-Y^2$ into two factors in the derivation?

Answer choices for question 12 A $(X-Y)(X+Y)$ B $(X-Y)^2$ C $(X+Y)^2$ D $X(X-Y)$